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    <id>1122</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>deu</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2009-03-04</completedDate>
    <publishedDate>2009-03-04</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="deu">Veränderungen der Publikations- und Kommunikationswelt: Open Access, Google, etc.</title>
    <title language="eng">Changes in the world of publishing and communication: Open Access, Google etc.</title>
    <abstract language="deu">Vorbemerkung Beim Schreiben dieses Artikels, der auf Veränderungen der Kommunikations- und Publikationstechniken und ihre Bedeutung hinweist, ist uns mehr als je zuvor bewusst geworden, wie beschränkt das Medium Papier ist. Es gibt z. B. keine Hyperlinks, durch die man unmittelbar das Erwähnte erleben oder überprüfen kann. Ein schneller Wechsel vom Wort zum Bild, zum Ton oder Video ist nicht möglich. Wer will schon lange URLs abtippen und Medienbrüche erleiden? Wir haben uns daher entschlossen, eine textidentische Version dieses Artikels mit allen URLs – sie liegt Ihnen hier vor – elektronisch anzubieten und in der für die "Gegenworte" (BBAW) gekürzten Fassung nur durch [URL] anzudeuten, dass der Leser an dieser Stelle einfach in der elektronischen Version einen Klick ins Internet machen sollte. Und damit sind wir bereits mitten im Thema.</abstract>
    <identifier type="serial">09-10</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1170</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-11223</identifier>
    <enrichment key="SourceTitle">Erschienen in Gegenworte: Hefte für den Disput über Wissen, 21. Heft, Frühjahr 2009, S. 69-72.</enrichment>
    <author>Martin Grötschel</author>
    <submitter>unknown unknown</submitter>
    <author>Joachim Lügger</author>
    <series>
      <title>ZIB-Report</title>
      <number>09-10</number>
    </series>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Publikations- und Kommunikationstechniken</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Open Access</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>techniques of publishing and communication</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Open Access</value>
    </subject>
    <collection role="ddc" number="020">Bibliotheks- und Informationswissenschaften</collection>
    <collection role="ccs" number="H.3.3">Information Search and Retrieval</collection>
    <collection role="ccs" number="H.3.5">Online Information Services</collection>
    <collection role="institutes" number="sis">Digital Data and Information for Society, Science, and Culture</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1122/ZR_09_10.pdf</file>
  </doc>
  <doc>
    <id>1145</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>deu</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2009-09-16</completedDate>
    <publishedDate>2009-09-16</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="deu">E-Learning and the Working Mathematician</title>
    <abstract language="deu">Eigentlich war der erste Autor nur zu einem Grußwort zur Tagung „GML² 2009 - Grundfragen Multi¬medialen Lehrens und Lernens“ eingeladen. Daraus wurde ein E-Learning-bezogener Vortrag, der – basierend auf Erfahrungen im Fach Mathematik – einen kritischen Blick auf die E-Learning-Szene in Deutschland wirft und diese mit entsprechenden Aktivitäten weltweit vergleicht. Dies ist die in seinen mathematischen Teilen gekürzte, in den E-Learning-Anteilen ein wenig erweiterte schriftliche Fassung des Vortrags. Der Artikel stammt nicht von E-Learning-Spezialisten sondern von Personen, die sich seit fast zwanzig Jahren mit elektronischer Information und Kommunikation (kurz: IuK) – insbesondere in der Mathematik – beschäftigen. Nach einer Definition von Michael Kerres kennzeichnet der Begriff E-Learning (electronic learning – elektronisch unterstütztes Lernen) alle Formen von Lernen, bei denen digitale Medien für die Präsentation und Distribution von Lernmaterialien und/oder zur Unterstützung zwischenmenschlicher Kommunikation zum Einsatz kommen, siehe z.B. http://de.wikipedia.org/wiki/E-Learning. IuK und E-Learning haben nach dieser Begriffsbildung viele Berührungspunkte. Deswegen wagen wir es, unsere positiven und negativen Erfahrungen im Bereich IuK in diesem Eröffnungsvortrag zu berichten, einige Entwicklungslinien zu vergleichen und eine eigene Kurzversion der Definition von E-Learning (besser E-Teaching and -Learning) voranzustellen: „Lehren und Lernen mit Unterstützung elektronischer Hilfsmittel“.</abstract>
    <identifier type="serial">09-29</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1194</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-11455</identifier>
    <identifier type="url">http://www.gml-2009.de/media/tagungsbandgml2009.pdf</identifier>
    <enrichment key="SourceTitle">Erschienen in: N. Apostolopoulos (Hrsg.): Tagungsband "GML² 2009 -- Grundfragen Multimedialen Lehrens und Lernens", Berlin 2009, S. 8-27.</enrichment>
    <author>Martin Grötschel</author>
    <submitter>unknown unknown</submitter>
    <author>Joachim Lügger</author>
    <submitter>unknown unknown</submitter>
    <submitter>unknown unknown</submitter>
    <series>
      <title>ZIB-Report</title>
      <number>09-29</number>
    </series>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>E-Learning</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>elektronisches Lehren und Lernen</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>e-learning</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>electronic learning</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="institutes" number="sis">Digital Data and Information for Society, Science, and Culture</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1145/ZIB_Report_09_29.pdf</file>
  </doc>
  <doc>
    <id>828</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2004-12-22</completedDate>
    <publishedDate>2004-12-22</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Polynomial Inequalities Representing Polyhedra</title>
    <abstract language="eng">Our main result is that every $n$-dimensional polytope can be described by at most $2n-1$ polynomial inequalities and, moreover, these polynomials can explicitly be constructed. For an $n$-dimensional pointed polyhedral cone we prove the bound $2n-2$ and for arbitrary polyhedra we get a constructible representation by $2n$ polynomial inequalities.</abstract>
    <identifier type="serial">04-53</identifier>
    <identifier type="opus3-id">829</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-8284</identifier>
    <enrichment key="SourceTitle">Appeared in: Mathematical Programming 103 (2005) 35-44</enrichment>
    <author>Hartwig Bosse</author>
    <author>Martin Grötschel</author>
    <author>Martin Henk</author>
    <series>
      <title>ZIB-Report</title>
      <number>04-53</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>polyhedra and polytopes</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>semi-algebraic sets</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>polyhedral combinatorics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>polynomial inequalities</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>stability index</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="14P10">Semialgebraic sets and related spaces</collection>
    <collection role="msc" number="52B11">n-dimensional polytopes</collection>
    <collection role="msc" number="52B55">Computational aspects related to convexity (For computational geometry and algorithms, see 68Q25, 68U05; for numerical algorithms, see 65Yxx) [See also 68Uxx]</collection>
    <collection role="msc" number="90C27">Combinatorial optimization</collection>
    <collection role="msc" number="90C57">Polyhedral combinatorics, branch-and-bound, branch-and-cut</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/828/ZR-04-53.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/828/ZR-04-53.pdf</file>
  </doc>
  <doc>
    <id>891</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>deu</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2005-12-14</completedDate>
    <publishedDate>2005-12-14</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="deu">Das Problem mit der Komplexität: P = NP?</title>
    <abstract language="deu">Was Komplexität ist, weiß niemand so richtig. In vielen Wissenschaftsgebieten wird der Begriff Komplexität verwendet, überall mit etwas anderer Bedeutung. Mathematik und Informatik hab en eine eigene Theorie hierzu entwickelt: die Komplexitätstheorie. Sie stellt zwar grundlegende Begriffe bereit, aber leider sind die meisten wichtigen Fragestellungen noch ungelöst. Diese kurze Einführung konzentriert sich auf einen speziellen, aber bedeutenden Aspekt der Theorie: Lösbarkeit von Problemen in deterministischer und nichtdeterministischer polynomialer Zeit. Hinter der für Uneingeweihte etwas kryptischen Frage "P = NP?" verbirgt sich das derzeit wichtigste Problem der Komplexitätstheorie. Anhand dieser Fragestellung werden einige Aspekte der Theorie erläutert und formell erklärt, was "P = NP?" bedeutet. Es geht nicht nur um komplizierte algorithmische Mathematik und Informatik, sondern um grundsätzliche Fragen unserer Lebensumwelt. Kann man vielleicht beweisen, dass es für viele Probleme unseres Alltags keine effizienten Lösungsmethoden gibt?</abstract>
    <identifier type="serial">05-58</identifier>
    <identifier type="opus3-id">891</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-8916</identifier>
    <enrichment key="SourceTitle">Ersch. in: Kombinatorische Optimierung erleben - In Studium und Unterricht von Stefan Hußmann und Brigitte Lutz-Westphal. Aus der Reihe: Mathematik erleben. Unter Mitarbeit von Brieden, Andreas / Gritzmann, Peter / Grötschel, Martin / Leuders, Timo. Vieweg, 2007. ISBN: 978-3-528-03216-6 S.265-274</enrichment>
    <author>Martin Grötschel</author>
    <series>
      <title>ZIB-Report</title>
      <number>05-58</number>
    </series>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Komplexität</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Komplexitätstheorie</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="68-01">Instructional exposition (textbooks, tutorial papers, etc.)</collection>
    <collection role="msc" number="68Q25">Analysis of algorithms and problem complexity [See also 68W40]</collection>
    <collection role="msc" number="97-01">Instructional exposition (textbooks, tutorial papers, etc.)</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/891/ZR-05-58.pdf</file>
  </doc>
  <doc>
    <id>852</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2005-03-17</completedDate>
    <publishedDate>2005-03-17</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Column-Generation Approach to Line Planning in Public Transport</title>
    <abstract language="eng">The line planning problem is one of the fundamental problems in strategic planning of public and rail transport. It consists in finding lines and corresponding frequencies in a transport network such that a given travel demand can be satisfied. There are (at least) two objectives. The transport company wishes to minimize operating costs, the passengers want to minimize travel times. We propose a n ew multi-commodity flow model for line planning. Its main features, in comparison to existing models, are that the passenger paths can be freely routed and that the lines are generated dynamically. We discuss properties of this model and investigate its complexity. Results with data for the city of Potsdam, Germany, are reported.</abstract>
    <identifier type="serial">05-18</identifier>
    <identifier type="opus3-id">852</identifier>
    <identifier type="doi">/10.1287/trsc.1060.0161</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-8522</identifier>
    <enrichment key="SourceTitle">Appeared in: Transportation Science 41 (2007) 123-132</enrichment>
    <author>Ralf Borndörfer</author>
    <author>Martin Grötschel</author>
    <author>Marc Pfetsch</author>
    <series>
      <title>ZIB-Report</title>
      <number>05-18</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>line planning</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>column generation</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="90B06">Transportation, logistics</collection>
    <collection role="msc" number="90C27">Combinatorial optimization</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <collection role="projects" number="MATHEON-B1">MATHEON-B1</collection>
    <collection role="projects" number="MATHEON-B15">MATHEON-B15</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/852/ZR-05-18.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/852/ZR_05_18.orig.Vers.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/852/ZR-05-18.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/852/ZR_05_18.orig.Vers.ps</file>
  </doc>
  <doc>
    <id>856</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2005-03-23</completedDate>
    <publishedDate>2005-03-23</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Public Transport to the fORe!</title>
    <abstract language="eng">Can OR methods help the public transport industry to break even? The article gives evidence that there exist significant potentials in this direction, which can be harnessed by a combination of modern mathematical methods and local planning knowledge. Many of the planning steps in public transport are classical combinatorial problems, which can be solved in unprecedented size and quality due the rapid progress in large-scale optimization. Three examples on vehicle scheduling, duty scheduling, and integrated vehicle and duty scheduling illustrate the level that has been reached and the improvements that can be achieved today. Extensions of such methods to further questions of strategic, online, and market-oriented planning are currently investigated. In this way, OR can make a significant contribution to answer the basic but extremely difficult question ``What is a good public transport network?.</abstract>
    <identifier type="serial">05-22</identifier>
    <identifier type="opus3-id">856</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-8562</identifier>
    <identifier type="url">http://www.lionhrtpub.com/orms/orms-4-06/frtransport.html</identifier>
    <enrichment key="SourceTitle">Appeared in: OR/MS Today, Apr 2006, Vol 33 (2), 30-40</enrichment>
    <author>Ralf Borndörfer</author>
    <author>Martin Grötschel</author>
    <author>Marc Pfetsch</author>
    <series>
      <title>ZIB-Report</title>
      <number>05-22</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Public transport</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>vehicle scheduling</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>duty scheduling</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="90B20">Traffic problems</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <collection role="projects" number="MATHEON-B1">MATHEON-B1</collection>
    <collection role="projects" number="MATHEON-B15">MATHEON-B15</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/856/ZR-05-22.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/856/ZR-05-22.ps</file>
  </doc>
  <doc>
    <id>857</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>deu</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2005-04-06</completedDate>
    <publishedDate>2005-04-06</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="deu">Entwicklung und Aufbau des Internet-Dienstes "Math&amp;Industry"</title>
    <abstract language="deu">Die Anwendung mathematischer Methoden und Verfahren wird immer mehr zur Voraussetzung innovativer Produkte und Dienstleistungen. Um neue Produkte und Dienstleistungen zu entwickeln, müssen die Produktions- und technologischen Prozesse mathematisch modelliert, beschrieben und optimiert werden. Diesen Umstand Rechnung tragend, hat das Bundesministerium für Bildung und Forschung (BMBF) 1993 begonnen, den Einsatz mathematischer Verfahren und Methoden in der Mathematik über ein spezielles Mathematikprogramm zu fördern. Inzwischen hat die vierte Förderperiode des Mathematikprogramms begonnen. \par Das Medium Internet und insbesondere das WWW sind für die Sichtbarkeit und Transparenz wissenschaftlicher Resultate in den letzten zehn Jahren immer wichtiger geworden. Wer nicht im Web "'sichtbar"' ist, läuft Gefahr, nicht wahrgenommen zu werden. Intention und Ziel des durchgeführten Projekts war es, ein Konzept für eine qualitativ hochwertige und umfassende Darstellung des BMBF Mathematikprogramms, insbesondere der in den Projekten erzielten Ergebnisse, zu entwickeln und zu realisieren und damit den Stellenwert und die Akzeptanz mathematischer Forschung in der Gesellschaft zu festigen und den Wissenstransfer zwischen mathematischer Forschung sowie Forschung und Entwicklung in der Wirtschaft und dem Dienstleistungsbereich zu fördern.</abstract>
    <identifier type="serial">05-23</identifier>
    <identifier type="opus3-id">857</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-8573</identifier>
    <author>Martin Grötschel</author>
    <author>Robert Roggenbuck</author>
    <author>Wolfram Sperber</author>
    <series>
      <title>ZIB-Report</title>
      <number>05-23</number>
    </series>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Internet services</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>distributed systems</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>XML</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>RDF</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/857/ZR-05-23.pdf</file>
  </doc>
  <doc>
    <id>890</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>deu</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2005-12-14</completedDate>
    <publishedDate>2005-12-14</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="deu">Schnelle Rundreisen: Das Travelling Salesman-Problem</title>
    <abstract language="deu">Das Travelling-Salesman-Problem (TSP) ist das am intensivsten untersuchte kombinatorische Optimierungsproblem. In diesem Abschnitt wird eine Einführung in das TSP gegeben. Es werden Problemstellungen erläutert, Anwendungen skizziert und einige Schwierigkeiten bei der korrekten Modellierung der Zielfunktion dargelegt. Es ist gar nicht so klar, was in einem konkreten Problem die wirkliche Entfernung ist. Exakte und approximative Lösungsverfahren werden an Beispielen skizziert, und es wird angedeutet, dass man, obwohl TSPs zu den theoretisch schweren Problemen zählen, in der Praxis TSPs von atemberaubender Größe lösen kann.</abstract>
    <identifier type="serial">05-57</identifier>
    <identifier type="opus3-id">890</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-8901</identifier>
    <enrichment key="SourceTitle">Ersch. in: Kombinatorische Optimierung erleben - In Studium und Unterricht von Stefan Hußmann und Brigitte Lutz-Westphal. Aus der Reihe: Mathematik erleben. Unter Mitarbeit von Brieden, Andreas / Gritzmann, Peter / Grötschel, Martin / Leuders, Timo. Vieweg, 2007. ISBN: 978-3-528-03216-6 S.95-128</enrichment>
    <author>Martin Grötschel</author>
    <series>
      <title>ZIB-Report</title>
      <number>05-57</number>
    </series>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Travelling-Salesman-Problem</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>TSP</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Rundreisen</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>optimale Tour</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="90-01">Instructional exposition (textbooks, tutorial papers, etc.)</collection>
    <collection role="msc" number="90C27">Combinatorial optimization</collection>
    <collection role="msc" number="97-01">Instructional exposition (textbooks, tutorial papers, etc.)</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/890/ZR-05-57.pdf</file>
  </doc>
  <doc>
    <id>914</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>deu</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2006-05-02</completedDate>
    <publishedDate>2006-05-02</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="deu">Ein gemischt-ganzzahliges lineares Optimierungsmodell für ein Laserschweißproblem im Karosseriebau</title>
    <abstract language="deu">Wir beschäftigen uns mit dem Problem der Betriebsplanung von Laserschweißrobotern im Karosseriebau. Gegeben ist eine Menge von Schweißnähten, die innerhalb einer Fertigungszelle an einem Karosserieteil gefertigt werden müssen. Die Schweißnähte werden durch mehrere parallel betriebene Roboter bearbeitet. Die Aufgabe besteht darin, für jeden Roboter eine Reihenfolge und eine zeitliche Koordinierung seiner Bewegungen zu finden, so dass alle Schweißnähte innerhalb der Taktzeit der Fertigungszelle bearbeitet werden und so wenig Laserquellen wie möglich eingesetzt werden. Dabei müssen einige Nebenbedingungen berücksichtigt werden. Für dieses spezielle Schweißproblem haben wir eine Formulierung als gemischt-ganzzahliges lineares Programm entwickelt, welches sich für die untersuchten praktischen Fälle sehr schnell lösen lässt.</abstract>
    <identifier type="serial">06-21</identifier>
    <identifier type="opus3-id">915</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-9141</identifier>
    <enrichment key="SourceTitle">Erschienen in: Zeitschrift für wirtschaftlichen Fabrikbetrieb (ZWF) Karosseriebau 101(5/2006) S. 260-264</enrichment>
    <author>Martin Grötschel</author>
    <author>Hinrich Hinrichs</author>
    <author>Klaus Schröer</author>
    <author>Andreas Tuchscherer</author>
    <series>
      <title>ZIB-Report</title>
      <number>06-21</number>
    </series>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Laserschweißen</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Gemischt-ganzzahlige Optimierung</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="ccs" number="G.2.0">General</collection>
    <collection role="msc" number="90B35">Scheduling theory, deterministic [See also 68M20]</collection>
    <collection role="msc" number="90C90">Applications of mathematical programming</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <collection role="projects" number="MATHEON-B14:Comb-Log">MATHEON-B14:Comb-Log</collection>
    <collection role="projects" number="RobotWelding">RobotWelding</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/914/ZR_06_21.en.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/914/ZR-06-21.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/914/ZR-06-21.ps</file>
  </doc>
  <doc>
    <id>917</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2006-05-05</completedDate>
    <publishedDate>2006-05-05</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Software for Teaching Modeling of Integer Programming Problems</title>
    <abstract language="eng">Modern applications of mathematical programming must take into account a multitude of technical details, business demands, and legal requirements. Teaching the mathematical modeling of such issues and their interrelations requires real-world examples that are well beyond the toy sizes that can be tackled with the student editions of most commercial software packages. We present a new tool, which is freely available for academic use including complete source code. It consists of an algebraic modeling language and a linear mixed integer programming solver. The performance and features of the tool are in the range of current state-of-the-art commercial tools, though not in all aspects as good as the best ones. Our tool does allow the execution and analysis of large real-world instances in the classroom and can therefore enhance the teaching of problem solving issues. Teaching experience has been gathered and practical usability was tested in classes at several universities and a two week intensive block course at TU Berlin. The feedback from students and teachers has been very positive.</abstract>
    <identifier type="serial">06-23</identifier>
    <identifier type="opus3-id">917</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-9176</identifier>
    <author>Tobias Achterberg</author>
    <author>Martin Grötschel</author>
    <author>Thorsten Koch</author>
    <series>
      <title>ZIB-Report</title>
      <number>06-23</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Integer Programming</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Modelling</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>MIP-Solver</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Algebraic Modelling Languages</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Teaching</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="68N99">None of the above, but in this section</collection>
    <collection role="msc" number="90-04">Explicit machine computation and programs (not the theory of computation or programming)</collection>
    <collection role="msc" number="90C11">Mixed integer programming</collection>
    <collection role="msc" number="97-04">Explicit machine computation and programs (not the theory of computation or programming)</collection>
    <collection role="msc" number="97U70">Technological tools. Calculators</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="achterberg">Achterberg, Tobias</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <collection role="persons" number="koch">Koch, Thorsten</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/917/ZR-06-23.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/917/ZR-06-23.ps</file>
  </doc>
  <doc>
    <id>2850</id>
    <completedYear>2000</completedYear>
    <publishedYear>2000</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>45</pageFirst>
    <pageLast>76</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>incollection</type>
    <publisherName>Vieweg Verlag</publisherName>
    <publisherPlace>Braunschweig/Wiesbaden</publisherPlace>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Der schnellste Weg zum Ziel</title>
    <parentTitle language="eng">Alles Mathematik</parentTitle>
    <identifier type="doi">10.1007/978-3-322-96366-6_5</identifier>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-4209</enrichment>
    <author>Ralf Borndörfer</author>
    <editor>Martin Aigner</editor>
    <author>Martin Grötschel</author>
    <editor>Ehrhard Behrends</editor>
    <author>Andreas Löbel</author>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <collection role="persons" number="loebel">Löbel, Andreas</collection>
    <collection role="projects" number="BMBF-DS">BMBF-DS</collection>
    <collection role="projects" number="MATHEON-B1">MATHEON-B1</collection>
    <collection role="projects" number="SenWiFo-Telebus">SenWiFo-Telebus</collection>
  </doc>
  <doc>
    <id>2865</id>
    <completedYear>2008</completedYear>
    <publishedYear>2008</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>127</pageFirst>
    <pageLast>153</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>bookpart</type>
    <publisherName>acatech – Deutsche Akademie der Technikwissenschaften und Springer</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Planungsprobleme im öffentlichen Verkehr</title>
    <parentTitle language="eng">PRODUKTIONSFAKTOR MATHEMATIK – Wie Mathematik Technik und Wirtschaft bewegt</parentTitle>
    <identifier type="url">http://opus.kobv.de/zib/volltexte/2008/1103/</identifier>
    <enrichment key="Series">acatech DISKUTIERT</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-10744</enrichment>
    <author>Ralf Borndörfer</author>
    <editor>Martin Grötschel</editor>
    <author>Martin Grötschel</author>
    <editor>Klaus Lucas</editor>
    <author>Ulrich Jaeger</author>
    <editor>Volker Mehrmann</editor>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <collection role="projects" number="MATHEON-B15">MATHEON-B15</collection>
  </doc>
  <doc>
    <id>2866</id>
    <completedYear>2008</completedYear>
    <publishedYear>2008</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>363</pageFirst>
    <pageLast>378</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>600</volume>
    <type>conferenceobject</type>
    <publisherName>Springer-Verlag</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Models for Line Planning in Public Transport</title>
    <parentTitle language="eng">Computer-aided Systems in Public Transport (CASPT 2004)</parentTitle>
    <identifier type="doi">10.1007/978-3-540-73312-6_18</identifier>
    <enrichment key="Series">Lecture Notes in Economics and Mathematical Systems</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-7854</enrichment>
    <author>Ralf Borndörfer</author>
    <editor>Mark Hickman</editor>
    <author>Martin Grötschel</author>
    <editor>Pitu Mirchandani</editor>
    <author>Marc Pfetsch</author>
    <editor>Stefan Voß</editor>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <collection role="projects" number="MATHEON-B1">MATHEON-B1</collection>
    <collection role="projects" number="MATHEON-B15">MATHEON-B15</collection>
  </doc>
  <doc>
    <id>2995</id>
    <completedYear>1973</completedYear>
    <publishedYear>1973</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>masterthesis</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Der Satz von Frobenius für konvergente Potenzreihen</title>
    <author>Martin Grötschel</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>2996</id>
    <completedYear>1975</completedYear>
    <publishedYear>1975</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>378</pageFirst>
    <pageLast>381</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>8</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Partial linear characterizations of the asymmetric travelling salesman polytope</title>
    <parentTitle language="eng">Mathematical Programming</parentTitle>
    <author>Martin Grötschel</author>
    <author>Manfred Padberg</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>2997</id>
    <completedYear>1976</completedYear>
    <publishedYear>1976</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>119</pageFirst>
    <pageLast>121</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>5</volume>
    <type>conferenceobject</type>
    <publisherName>Physica-Verlag</publisherName>
    <publisherPlace>Würzburg</publisherPlace>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Über Graphen mit Kreisen, die gegebene Wege enthalten</title>
    <parentTitle language="eng">Proceedings in Operations Research</parentTitle>
    <author>Martin Grötschel</author>
    <editor>Jürg Kohlas</editor>
    <editor>Olaf Seifert</editor>
    <editor>H. Zimmermann</editor>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>2998</id>
    <completedYear>1977</completedYear>
    <publishedYear>1977</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>233</pageFirst>
    <pageLast>245</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>1</volume>
    <type>bookpart</type>
    <publisherName>North-Holland</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Graphs with cycles containing given paths</title>
    <parentTitle language="eng">Studies in Integer Programming</parentTitle>
    <enrichment key="Series">Annals of Discrete Mathematics</enrichment>
    <author>Martin Grötschel</author>
    <editor>Peter Hammer</editor>
    <editor>Ellis Johnson</editor>
    <editor>Bernhard Korte</editor>
    <editor>George Nemhauser</editor>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>2999</id>
    <completedYear>1977</completedYear>
    <publishedYear>1977</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>36</volume>
    <type>book</type>
    <publisherName>Verlag Anton Hain</publisherName>
    <publisherPlace>Meisenheim am Glan</publisherPlace>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Polyedrische Charakterisierungen kombinatorischer Optimierungsprobleme</title>
    <parentTitle language="eng">Mathematical Systems in Economics</parentTitle>
    <identifier type="isbn">3-445-01537-6</identifier>
    <author>Martin Grötschel</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3000</id>
    <completedYear>1977</completedYear>
    <publishedYear>1977</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>72</pageFirst>
    <pageLast>84</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">The monotone 2-matching polytope on a complete graph</title>
    <parentTitle language="eng">Operations Research Verfahren XXIV, Symposium in Mannheim</parentTitle>
    <author>Martin Grötschel</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3001</id>
    <completedYear>1977</completedYear>
    <publishedYear>1977</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>306</pageFirst>
    <pageLast>313</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Facetten von Matroid-Polytopen</title>
    <parentTitle language="eng">Operations Research Verfahren XXV, Symposium Heidelberg 1976</parentTitle>
    <author>Martin Grötschel</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3002</id>
    <completedYear>1977</completedYear>
    <publishedYear>1977</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>457</pageFirst>
    <pageLast>467</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>bookpart</type>
    <publisherName>J. C. B. Mohr</publisherName>
    <publisherPlace>Tübingen</publisherPlace>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Bemerkungen zur Optimierung ökonomischer Modelle</title>
    <parentTitle language="eng">Quantitative Wirtschaftsforschung, Willhelm Krelle zum 60. Geburtstag</parentTitle>
    <author>Martin Grötschel</author>
    <editor>Horst Albach</editor>
    <author>Bernhard Korte</author>
    <editor>Ernst Helmstädter</editor>
    <editor>Rudolf Henn</editor>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3003</id>
    <completedYear>1977</completedYear>
    <publishedYear>1977</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>33</pageFirst>
    <pageLast>64</pageLast>
    <pageNumber/>
    <edition/>
    <issue>1</issue>
    <volume>21</volume>
    <type>article</type>
    <publisherName>Physica-Verlag</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Lineare Charakterisierungen von Travelling Salesman Problemen</title>
    <parentTitle language="eng">Zeitschrift für Operations Research, Series A</parentTitle>
    <author>Martin Grötschel</author>
    <author>Manfred Padberg</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3004</id>
    <completedYear>1978</completedYear>
    <publishedYear>1978</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>T469</pageFirst>
    <pageLast>T471</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>58</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
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    <title language="eng">Hypo-Hamiltonian Facets of the Symmetric Travelling Salesman Polytope</title>
    <parentTitle language="eng">Zeitschrift für Angewandte Mathematik und Mechanik</parentTitle>
    <author>Martin Grötschel</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
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    <completedYear>1978</completedYear>
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    <language>eng</language>
    <pageFirst>105</pageFirst>
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    <edition/>
    <issue/>
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    <title language="eng">On the symmetric travelling salesman problem</title>
    <parentTitle language="eng">Optimization and operations research, Proc. Workshop, Bonn 1977</parentTitle>
    <enrichment key="Series">Lecture Notes in Economics and Mathematical Systems</enrichment>
    <author>Martin Grötschel</author>
    <editor>Rudolf Henn</editor>
    <author>Manfred Padberg</author>
    <editor>Bernhard Korte</editor>
    <editor>W. Oettli</editor>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
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    <completedYear>1978</completedYear>
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    <language>eng</language>
    <pageFirst>373</pageFirst>
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    <edition/>
    <issue/>
    <volume>14</volume>
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    <title language="eng">A property of continuous unbounded algorithms</title>
    <parentTitle language="eng">Mathematical Programming</parentTitle>
    <author>Martin Grötschel</author>
    <author>Rabe von Randow</author>
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    <id>3007</id>
    <completedYear>1979</completedYear>
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    <language>eng</language>
    <pageFirst>213</pageFirst>
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    <edition/>
    <issue/>
    <volume>3</volume>
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    <title language="eng">On minimal strong blocks</title>
    <parentTitle language="eng">Journal of Graph Theory</parentTitle>
    <author>Martin Grötschel</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
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  <doc>
    <id>3008</id>
    <completedYear>1979</completedYear>
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    <language>eng</language>
    <pageFirst>112</pageFirst>
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    <pageNumber/>
    <edition/>
    <issue/>
    <volume>46</volume>
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    <publisherName>Birkhäuser</publisherName>
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    <title language="eng">Strong blocks and the optimum branching problem</title>
    <parentTitle language="eng">Numerische Methoden bei graphentheoretischen und kombinatorischen Problemen, Bd. 2, Tagung in Oberwolfach 1978</parentTitle>
    <enrichment key="Series">ISNM International Series of Numerical Mathematics</enrichment>
    <author>Martin Grötschel</author>
    <editor>Lothar Collatz</editor>
    <editor>G. Meinardus</editor>
    <editor>W. Wetterling (Hrsg.)</editor>
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    <language>eng</language>
    <pageFirst>221</pageFirst>
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    <title language="eng">The Graphs for which All Strong Orientations Are Hamiltonian</title>
    <parentTitle language="eng">Journal of Graph Theory</parentTitle>
    <author>Martin Grötschel</author>
    <author>Frank Harary</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
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  <doc>
    <id>3010</id>
    <completedYear>1979</completedYear>
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    <language>eng</language>
    <pageFirst>265</pageFirst>
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    <edition/>
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    <volume>16</volume>
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    <title language="eng">On the symmetric travelling salesman problem I</title>
    <parentTitle language="eng">Mathematical Programming</parentTitle>
    <author>Martin Grötschel</author>
    <author>Manfred Padberg</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
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    <id>3011</id>
    <completedYear>1979</completedYear>
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    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>281</pageFirst>
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    <edition/>
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    <volume>16</volume>
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    <title language="eng">On the symmetric travelling salesman problem II</title>
    <parentTitle language="eng">Mathematical Programming</parentTitle>
    <author>Martin Grötschel</author>
    <author>Manfred Padberg</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
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    <id>3012</id>
    <completedYear>1980</completedYear>
    <publishedYear>1980</publishedYear>
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    <language>eng</language>
    <pageFirst>61</pageFirst>
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    <edition/>
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    <volume>12</volume>
    <type>article</type>
    <publisherName>North-Holland</publisherName>
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    <title language="eng">On the symmetric travelling salesman problem</title>
    <parentTitle language="eng">Mathematical Programming Study</parentTitle>
    <author>Martin Grötschel</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
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    <id>3013</id>
    <completedYear>1980</completedYear>
    <publishedYear>1980</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>285</pageFirst>
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    <pageNumber/>
    <edition/>
    <issue>2</issue>
    <volume>5</volume>
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    <title language="eng">On the monotone symmetric travelling salesman problem</title>
    <parentTitle language="eng">Mathematics of Operations Research</parentTitle>
    <author>Martin Grötschel</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
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    <id>3064</id>
    <completedYear>1990</completedYear>
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    <language>eng</language>
    <pageFirst>271</pageFirst>
    <pageLast>284</pageLast>
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    <publisherName>Physica-Verlag</publisherName>
    <publisherPlace>Heidelberg</publisherPlace>
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    <title language="eng">Composition of facets of the clique partitioning polytope</title>
    <parentTitle language="eng">Topics in combinatorics and graph theory. Essays in honour of Gerhard Ringel</parentTitle>
    <author>Martin Grötschel</author>
    <editor>Rainer Bodendiek</editor>
    <author>Yoshiko Wakabayashi</author>
    <editor>Rudolf Henn</editor>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
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    <id>3054</id>
    <completedYear>1987</completedYear>
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    <language>eng</language>
    <pageFirst>325</pageFirst>
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    <publisherName>Springer</publisherName>
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    <title language="eng">Calculating Exact Ground States of Spin Glasses</title>
    <parentTitle language="eng">Proceedings of the Heidelberg Colloquium on “Glassy Dynamics”, Lecture Notes in Physics 275</parentTitle>
    <author>Martin Grötschel</author>
    <editor>J. van Hemmen</editor>
    <author>Michael Jünger</author>
    <editor>I. Morgenstern</editor>
    <author>Gerhard Reinelt</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
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    <id>3055</id>
    <completedYear>1988</completedYear>
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    <language>eng</language>
    <pageFirst>493</pageFirst>
    <pageLast>513</pageLast>
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    <edition/>
    <issue>3</issue>
    <volume>36</volume>
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    <title language="eng">An application of combinatorial optimization to statistical physics and circuit layout design</title>
    <parentTitle language="eng">Operations Research</parentTitle>
    <author>Francisco Barahona</author>
    <author>Martin Grötschel</author>
    <author>Michael Jünger</author>
    <author>Gerhard Reinelt</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
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    <id>3056</id>
    <completedYear>1988</completedYear>
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    <language>eng</language>
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    <edition/>
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    <title language="eng">Geometric Algorithms and Combinatorial Optimization</title>
    <parentTitle language="eng">Algorithms and Combinatorics</parentTitle>
    <identifier type="isbn">3-540-13624-X, 0-387-13624-X (U.S.)</identifier>
    <author>Martin Grötschel</author>
    <author>Lászlo Lovász</author>
    <author>Alexander Schrijver</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
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    <id>3057</id>
    <completedYear>1989</completedYear>
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    <language>eng</language>
    <pageFirst>393</pageFirst>
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    <edition/>
    <issue>11</issue>
    <volume>69</volume>
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    <title language="eng">Via Minimization with Pin Preassignments and Layer Preference</title>
    <parentTitle language="eng">ZAMM – Zeitschrift für Angewandte Mathematik und Mechanik</parentTitle>
    <author>Martin Grötschel</author>
    <author>Michael Jünger</author>
    <author>Gerhard Reinelt</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
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    <id>3058</id>
    <completedYear>1989</completedYear>
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    <language>eng</language>
    <pageFirst>306</pageFirst>
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    <volume>46</volume>
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    <title language="eng">Decomposition and Optimization over Cycles in Binary Matroids</title>
    <parentTitle language="eng">Journal of Combinatorial Theory, Series B</parentTitle>
    <author>Martin Grötschel</author>
    <author>Klaus Truemper</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
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    <id>3059</id>
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    <language>eng</language>
    <pageFirst>523</pageFirst>
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    <title language="eng">Master Polytopes for Cycles of Binary Matroids</title>
    <parentTitle language="eng">Linear Algebra and its Applications</parentTitle>
    <author>Martin Grötschel</author>
    <author>Klaus Truemper</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
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    <id>3060</id>
    <completedYear>1989</completedYear>
    <publishedYear>1989</publishedYear>
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    <language>eng</language>
    <pageFirst>59</pageFirst>
    <pageLast>96</pageLast>
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    <volume>45</volume>
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    <publisherName>Mathematical Programming, Series B</publisherName>
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    <title language="eng">A cutting plane algorithm for a clustering problem</title>
    <parentTitle language="eng">Mathematical Programming, Series B</parentTitle>
    <author>Martin Grötschel</author>
    <author>Yoshiko Wakabayashi</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
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    <completedYear>1990</completedYear>
    <publishedYear>1990</publishedYear>
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    <language>eng</language>
    <pageFirst>19</pageFirst>
    <pageLast>28</pageLast>
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    <publisherName>University of Waterloo Press</publisherName>
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    <title language="eng">On Identifying in Polynomial Time Violated Subtour Elimination and Precedence Forcing Constraints for the Sequential Ordering Problem</title>
    <parentTitle language="eng">Integer Programming and Combinatorial Optimization, Proceeedings of a Conference held at the University of Waterloo, May 28-30, 1990</parentTitle>
    <author>Norbert Ascheuer</author>
    <editor>Ravi Kannan</editor>
    <author>Laureano Escudero</author>
    <editor>William Pulleyblank</editor>
    <author>Martin Grötschel</author>
    <author>Mechthild Stoer</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
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    <id>3062</id>
    <completedYear>1990</completedYear>
    <publishedYear>1990</publishedYear>
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    <language>eng</language>
    <pageFirst>502</pageFirst>
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    <title language="eng">Integer Polyhedra Arising from Certain Network Design Problems with Connectivity Constraints</title>
    <parentTitle language="eng">SIAM Journal on Discrete Mathematics</parentTitle>
    <author>Martin Grötschel</author>
    <author>Clyde Monma</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
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    <id>3063</id>
    <completedYear>1990</completedYear>
    <publishedYear>1990</publishedYear>
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    <language>eng</language>
    <pageFirst>367</pageFirst>
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    <edition/>
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    <volume>47</volume>
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    <title language="eng">Facets of the clique partitioning polytope</title>
    <parentTitle language="eng">Mathematical Programming, Series A</parentTitle>
    <author>Martin Grötschel</author>
    <author>Yoshiko Wakabayashi</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
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    <id>3034</id>
    <completedYear>1984</completedYear>
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    <language>eng</language>
    <pageFirst>261</pageFirst>
    <pageLast>295</pageLast>
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    <edition/>
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    <volume>25</volume>
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    <title language="eng">Optimal triangulation of large real world input-output matrices</title>
    <parentTitle language="eng">Statistische Hefte</parentTitle>
    <author>Martin Grötschel</author>
    <author>Michael Jünger</author>
    <author>Gerhard Reinelt</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
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    <id>3035</id>
    <completedYear>1984</completedYear>
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    <language>eng</language>
    <pageFirst>167</pageFirst>
    <pageLast>183</pageLast>
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    <publisherName>Academic Press</publisherName>
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    <title language="eng">Geometric Methods in Combinatorial Optimization</title>
    <parentTitle language="eng">Progress in Combinatorial Optimization, (Conference Waterloo/Ontario 1982)</parentTitle>
    <author>Martin Grötschel</author>
    <editor>William Pulleyblank</editor>
    <author>Lászlo Lovász</author>
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    <id>3036</id>
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    <language>eng</language>
    <pageFirst>325</pageFirst>
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    <edition/>
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    <volume>21</volume>
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    <publisherName>North-Holland</publisherName>
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    <title language="eng">Polynomial algorithms for perfect graphs</title>
    <parentTitle language="eng">Topics on perfect graphs</parentTitle>
    <enrichment key="Series">Annals of Discrete Mathematics</enrichment>
    <author>Martin Grötschel</author>
    <editor>Claude Berge</editor>
    <author>Lászlo Lovász</author>
    <editor>Vašek Chvátal</editor>
    <author>Alexander Schrijver</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3037</id>
    <completedYear>1984</completedYear>
    <publishedYear>1984</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>291</pageFirst>
    <pageLast>295</pageLast>
    <pageNumber/>
    <edition/>
    <issue>4</issue>
    <volume>4</volume>
    <type>article</type>
    <publisherName/>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Corrigendum to our paper “The ellipsoid method and its consequences in combinatorial optimization”</title>
    <parentTitle language="eng">Combinatorica</parentTitle>
    <author>Martin Grötschel</author>
    <author>Lászlo Lovász</author>
    <author>Alexander Schrijver</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3038</id>
    <completedYear>1984</completedYear>
    <publishedYear>1984</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>28</pageFirst>
    <pageLast>40</pageLast>
    <pageNumber/>
    <edition/>
    <issue>1</issue>
    <volume>29</volume>
    <type>article</type>
    <publisherName>North-Holland</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A polynomial algorithm for the max-cut problem on graphs without long odd cycles</title>
    <parentTitle language="eng">Mathematical Programming</parentTitle>
    <author>Martin Grötschel</author>
    <author>George Nemhauser</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3039</id>
    <completedYear>1984</completedYear>
    <publishedYear>1984</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>147</pageFirst>
    <pageLast>175</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName>North-Holland</publisherName>
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    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Constructions of hypotraceable digraphs</title>
    <parentTitle language="eng">Mathematical Programming. Proceedings of the International Congress on Mathematical Programming, Rio de Janeiro, Brazil, 6-8 April 1981</parentTitle>
    <author>Martin Grötschel</author>
    <editor>Richard Cottle</editor>
    <author>Yoshiko Wakabayashi</author>
    <editor>Milton Kelmanson</editor>
    <editor>Bernhard Korte</editor>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3040</id>
    <completedYear>1985</completedYear>
    <publishedYear>1985</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>340</pageFirst>
    <pageLast>358</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>10</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Facets of the Bipartite Subgraph Polytope</title>
    <parentTitle language="eng">Mathematics of Operations Research</parentTitle>
    <author>Francisco Barahona</author>
    <author>Martin Grötschel</author>
    <author>Ali Mahjoub</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3041</id>
    <completedYear>1985</completedYear>
    <publishedYear>1985</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>243</pageFirst>
    <pageLast>259</pageLast>
    <pageNumber/>
    <edition/>
    <issue>3</issue>
    <volume>33</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Solving matching problems with linear programming</title>
    <parentTitle language="eng">Mathematical Programming</parentTitle>
    <author>Martin Grötschel</author>
    <author>Olaf Holland</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3042</id>
    <completedYear>1985</completedYear>
    <publishedYear>1985</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>217</pageFirst>
    <pageLast>264</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName>D. Reidel Publishing Company</publisherName>
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    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Acyclic subdigraphs and linear orderings</title>
    <parentTitle language="eng">Graphs and Order. The Role of Graphs in the Theory of Ordered Sets and its Applications, Proceedings of NATO ASI, Ser. C 147, Banff/Canada 1984</parentTitle>
    <author>Martin Grötschel</author>
    <editor>Ivan Rival</editor>
    <author>Michael Jünger</author>
    <author>Gerhard Reinelt</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3043</id>
    <completedYear>1985</completedYear>
    <publishedYear>1985</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>28</pageFirst>
    <pageLast>42</pageLast>
    <pageNumber/>
    <edition/>
    <issue>1</issue>
    <volume>33</volume>
    <type>article</type>
    <publisherName>North-Holland</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">On the acyclic subgraph polytope</title>
    <parentTitle language="eng">Mathematical Programming</parentTitle>
    <author>Martin Grötschel</author>
    <author>Michael Jünger</author>
    <author>Gerhard Reinelt</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3044</id>
    <completedYear>1985</completedYear>
    <publishedYear>1985</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>43</pageFirst>
    <pageLast>60</pageLast>
    <pageNumber/>
    <edition/>
    <issue>1</issue>
    <volume>33</volume>
    <type>article</type>
    <publisherName>North-Holland</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Facets of the linear ordering polytope</title>
    <parentTitle language="eng">Mathematical Programming</parentTitle>
    <author>Martin Grötschel</author>
    <author>Michael Jünger</author>
    <author>Gerhard Reinelt</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3045</id>
    <completedYear>1985</completedYear>
    <publishedYear>1985</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>251</pageFirst>
    <pageLast>306</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>bookpart</type>
    <publisherName>Wiley</publisherName>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Polyhedral theory</title>
    <parentTitle language="eng">The Traveling Salesman Problem. A Guided Tour of Combinatorial Optimization</parentTitle>
    <author>Martin Grötschel</author>
    <editor>Eugene Lawler</editor>
    <author>Manfred Padberg</author>
    <editor>Jan Lenstra</editor>
    <editor>Alexander Kan</editor>
    <editor>David Shmoys</editor>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3046</id>
    <completedYear>1985</completedYear>
    <publishedYear>1985</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>307</pageFirst>
    <pageLast>360</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>bookpart</type>
    <publisherName>Wiley</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Polyhedral computations</title>
    <parentTitle language="eng">The Traveling Salesman Problem. A Guided Tour of Combinatorial Optimization</parentTitle>
    <author>Manfred Padberg</author>
    <editor>Eugene Lawler</editor>
    <author>Martin Grötschel</author>
    <editor>Jan Lenstra</editor>
    <editor>Alexander Kan</editor>
    <editor>David Shmoys</editor>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3047</id>
    <completedYear>1985</completedYear>
    <publishedYear>1985</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue>77</issue>
    <volume/>
    <type>report</type>
    <publisherName>Mathematisches Institut, Universität Augsburg</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">The Travelling Salesman Problem for Graphs not Contractible to K_5 - e</title>
    <author>Francisco Barahona</author>
    <author>Martin Grötschel</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3048</id>
    <completedYear>1986</completedYear>
    <publishedYear>1986</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>40</pageFirst>
    <pageLast>62</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>40</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">On the Cycle Polytope of a Binary Matroid</title>
    <parentTitle language="eng">Journal of Combinatorial Theory, Series B</parentTitle>
    <author>Francisco Barahona</author>
    <author>Martin Grötschel</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3049</id>
    <completedYear>1986</completedYear>
    <publishedYear>1986</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>69</pageFirst>
    <pageLast>100</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>21</volume>
    <type>conferenceobject</type>
    <publisherName>Institut für Mathematik, Universität Bayreuth</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Polyedrische Kombinatorik und Schnittebenenverfahren, Tagungsbericht 2. Sommerschule Diskrete Strukturen, Bayreuth 1985</title>
    <parentTitle language="eng">Diskrete Strukturen, algebraische Methoden und Anwendungen</parentTitle>
    <author>Martin Grötschel</author>
    <editor>Adalbert Kerber</editor>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3050</id>
    <completedYear>1986</completedYear>
    <publishedYear>1986</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>341</pageFirst>
    <pageLast>367</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>bookpart</type>
    <publisherName>Verlag Chemie</publisherName>
    <publisherPlace>Weinheim</publisherPlace>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Fortschritte in der polyedrischen Kombinatorik</title>
    <parentTitle language="eng">Ökonomische Prognose-, Entscheidungs- und Gleichgewichtsmodelle, Abschlußberichte des SFB 21</parentTitle>
    <author>Martin Grötschel</author>
    <editor>Wilhelm Krelle</editor>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3051</id>
    <completedYear>1986</completedYear>
    <publishedYear>1986</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>330</pageFirst>
    <pageLast>343</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>40</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Relaxations of Vertex Packing</title>
    <parentTitle language="eng">Journal of Combinatorial Theory, Series B</parentTitle>
    <author>Martin Grötschel</author>
    <author>Lászlo Lovász</author>
    <author>Alexander Schrijver</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3052</id>
    <completedYear>1986</completedYear>
    <publishedYear>1986</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>537</pageFirst>
    <pageLast>569</pageLast>
    <pageNumber/>
    <edition/>
    <issue>4</issue>
    <volume>11</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Clique tree inequalities and the symmetric travelling salesman problem</title>
    <parentTitle language="eng">Mathematics of Operations Research</parentTitle>
    <author>Martin Grötschel</author>
    <author>William Pulleyblank</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3053</id>
    <completedYear>1987</completedYear>
    <publishedYear>1987</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>327</pageFirst>
    <pageLast>344</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>39</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Cutting Plane Algorithm for Minimum Perfect 2-Matchings</title>
    <parentTitle language="eng">Computing</parentTitle>
    <author>Martin Grötschel</author>
    <author>Olaf Holland</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3014</id>
    <completedYear>1980</completedYear>
    <publishedYear>1980</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>377</pageFirst>
    <pageLast>381</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>4</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Hypotraceable digraphs</title>
    <parentTitle language="eng">Journal of Graph Theory</parentTitle>
    <author>Martin Grötschel</author>
    <author>Carsten Thomassen</author>
    <author>Yoshiko Wakabayashi</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3015</id>
    <completedYear>1980</completedYear>
    <publishedYear>1980</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>99</pageFirst>
    <pageLast>119</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>36</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Hypohamiltonian digraphs</title>
    <parentTitle language="eng">Methods of Operations Research</parentTitle>
    <author>Martin Grötschel</author>
    <author>Yoshiko Wakabayashi</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3016</id>
    <completedYear>1981</completedYear>
    <publishedYear>1981</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>book</type>
    <publisherName>Institut für Mittelstandsforschung</publisherName>
    <publisherPlace>Bonn</publisherPlace>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Input-Output-Analyse bei unternehmensgrößenspezifischen Fragestellungen</title>
    <author>Achim Bachem</author>
    <author>Lothar Butz</author>
    <author>Martin Grötschel</author>
    <author>Rainer (Bearb.)</author>
    <author>Bernhard Leitung)</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3017</id>
    <completedYear>1981</completedYear>
    <publishedYear>1981</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>215</pageFirst>
    <pageLast>219</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>40</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Homogenization of polyhedra</title>
    <parentTitle language="eng">Methods of Operations Research</parentTitle>
    <author>Achim Bachem</author>
    <author>Martin Grötschel</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3018</id>
    <completedYear>1981</completedYear>
    <publishedYear>1981</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1</pageFirst>
    <pageLast>22</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>14</volume>
    <type>conferenceobject</type>
    <publisherName>North-Holland</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Characterizations of adjacency of faces of polyhedra</title>
    <parentTitle language="eng">Mathematical Programming at Oberwolfach</parentTitle>
    <author>Achim Bachem</author>
    <editor>Heinz König</editor>
    <author>Martin Grötschel</author>
    <editor>Bernhard Korte</editor>
    <editor>Klaus Ritter</editor>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3019</id>
    <completedYear>1981</completedYear>
    <publishedYear>1981</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>169</pageFirst>
    <pageLast>197</pageLast>
    <pageNumber/>
    <edition/>
    <issue>2</issue>
    <volume>1</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">The ellipsoid method and its consequences in combinatorial optimization</title>
    <parentTitle language="eng">Combinatorica</parentTitle>
    <author>Martin Grötschel</author>
    <author>Lászlo Lovász</author>
    <author>Alexander Schrijver</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3020</id>
    <completedYear>1981</completedYear>
    <publishedYear>1981</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>511</pageFirst>
    <pageLast>546</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">The ellipsoid method and its consequences in combinatorial optimization</title>
    <parentTitle language="eng">IIASA Collab. Proceedings Ser. CP-81-S1</parentTitle>
    <author>Martin Grötschel</author>
    <author>Lászlo Lovász</author>
    <author>Alexander Schrijver</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3021</id>
    <completedYear>1981</completedYear>
    <publishedYear>1981</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>23</pageFirst>
    <pageLast>27</pageLast>
    <pageNumber/>
    <edition/>
    <issue>1</issue>
    <volume>1</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Weakly bipartite graphs and the max-cut problem</title>
    <parentTitle language="eng">Operations Research Letters</parentTitle>
    <author>Martin Grötschel</author>
    <author>William Pulleyblank</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3022</id>
    <completedYear>1981</completedYear>
    <publishedYear>1981</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>43</pageFirst>
    <pageLast>59</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>34</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">On the structure of the monotone asymmetric travelling salesman polytope I</title>
    <parentTitle language="eng">Discrete Mathematics</parentTitle>
    <author>Martin Grötschel</author>
    <author>Yoshiko Wakabayashi</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3023</id>
    <completedYear>1981</completedYear>
    <publishedYear>1981</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>77</pageFirst>
    <pageLast>97</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>14</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">On the structure of the monotone asymmetric travelling salesman polytope II</title>
    <parentTitle language="eng">Mathematical Programming Study</parentTitle>
    <author>Martin Grötschel</author>
    <author>Yoshiko Wakabayashi</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3024</id>
    <completedYear>1982</completedYear>
    <publishedYear>1982</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>51</pageFirst>
    <pageLast>106</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName>North-Holland</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">New aspects of polyhedral theory</title>
    <parentTitle language="eng">Modern Applied Mathematics</parentTitle>
    <author>Achim Bachem</author>
    <editor>Bernhard Korte</editor>
    <author>Martin Grötschel</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3026</id>
    <completedYear>1982</completedYear>
    <publishedYear>1982</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>437</pageFirst>
    <pageLast>515</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName>North-Holland</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Approaches to Hard Combinatorial Optimization Problems</title>
    <parentTitle language="eng">Modern Applied Mathematics, Optimization and Operations Research, Lect. Summer Sch., Bonn 1979</parentTitle>
    <author>Martin Grötschel</author>
    <editor>Bernhard Korte</editor>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3027</id>
    <completedYear>1982</completedYear>
    <publishedYear>1982</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>45</pageFirst>
    <pageLast>54</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName>Bouvier</publisherName>
    <publisherPlace>Bonn</publisherPlace>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Kombinatorische Optimierung</title>
    <parentTitle language="eng">Forschungsbericht 1978-1980 der Rheinischen Friedrich-Wilhelms-Universität</parentTitle>
    <author>Martin Grötschel</author>
    <editor>Der der Universität Bonn</editor>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3029</id>
    <completedYear>1984</completedYear>
    <publishedYear>1984</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>171</pageFirst>
    <pageLast>189</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName>Academic Press</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">On Intersections of Longest Cycles</title>
    <parentTitle language="eng">Graph Theory and Combinatorics</parentTitle>
    <author>Martin Grötschel</author>
    <editor>Béla Bollobás</editor>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3030</id>
    <completedYear>1984</completedYear>
    <publishedYear>1984</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>249</pageFirst>
    <pageLast>294</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>bookpart</type>
    <publisherName>Birkhäuser</publisherName>
    <publisherPlace>Basel</publisherPlace>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Developments in combinatorial optimization</title>
    <parentTitle language="eng">Perspectives in Mathematics (Anniversary of Oberwolfach 1984)</parentTitle>
    <author>Martin Grötschel</author>
    <editor>Willi Jäger</editor>
    <editor>J. Moser</editor>
    <editor>R. Remmert</editor>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3031</id>
    <completedYear>1984</completedYear>
    <publishedYear>1984</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1</pageFirst>
    <pageLast>10</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName>Wiley</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Polyhedral Combinatorics</title>
    <parentTitle language="eng">COMBINATORIAL OPTIMIZATION</parentTitle>
    <author>Martin Grötschel</author>
    <editor>Michael O’Heigeartaigh</editor>
    <editor>Jan Lenstra</editor>
    <editor>Alexander Kan</editor>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3032</id>
    <completedYear>1984</completedYear>
    <publishedYear>1984</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue>231</issue>
    <volume/>
    <type>report</type>
    <publisherName>Forschungszentrum Graz, Österreich</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Polyedrische Kombinatorik und Schnittebenenverfahren</title>
    <author>Martin Grötschel</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3033</id>
    <completedYear>1984</completedYear>
    <publishedYear>1984</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1195</pageFirst>
    <pageLast>1220</pageLast>
    <pageNumber/>
    <edition/>
    <issue>6</issue>
    <volume>32</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Cutting Plane Algorithm for the Linear Ordering Problem</title>
    <parentTitle language="eng">Operations Research</parentTitle>
    <author>Martin Grötschel</author>
    <author>Michael Jünger</author>
    <author>Gerhard Reinelt</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3174</id>
    <completedYear>2007</completedYear>
    <publishedYear>2007</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>123</pageFirst>
    <pageLast>132</pageLast>
    <pageNumber/>
    <edition/>
    <issue>1</issue>
    <volume>41</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Column-Generation Approach to Line Planning in Public Transport</title>
    <parentTitle language="eng">Transportation Science (INFORMS)</parentTitle>
    <identifier type="doi">10.1287/trsc.1060.0161</identifier>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-8522</enrichment>
    <author>Ralf Borndörfer</author>
    <author>Martin Grötschel</author>
    <author>Marc Pfetsch</author>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <collection role="projects" number="MATHEON-B1">MATHEON-B1</collection>
    <collection role="projects" number="MATHEON-B15">MATHEON-B15</collection>
  </doc>
  <doc>
    <id>219</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>deu</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1996-03-04</completedDate>
    <publishedDate>1996-03-04</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="deu">Optimierung des Fahrzeugumlaufs im Öffentlichen Nahverkehr</title>
    <abstract language="eng">This paper addresses the problem of scheduling vehicles in a public mass transportation system. We show how this problem can be modelled as a special multicommodity flow problem and outline the solution methodology we have developed. Based on polyhedral investigations, we have designed and implemented a branch&amp;cut algorithm and various heuristics with which real vehicle scheduling problems of truely large scale can be solved to optimality. We describe some implementation issues and report computational results.</abstract>
    <identifier type="serial">SC-96-08</identifier>
    <identifier type="opus3-id">219</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-2195</identifier>
    <enrichment key="SourceTitle">Erschienen in: Mathematik : Schlüsseltechnologie für die Zukunft; Verbundprojekte zwischen Universität und Industrie. K.-H. Hoffmann u.a. (Hrsg.) Berlin u.a.: Springer 1997. S. 609-624</enrichment>
    <author>Martin Grötschel</author>
    <author>Andreas Löbel</author>
    <author>Manfred Völker</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-96-08</number>
    </series>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <collection role="persons" number="loebel">Löbel, Andreas</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/219/SC-96-08.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/219/SC-96-08.pdf</file>
  </doc>
  <doc>
    <id>280</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1997-02-28</completedDate>
    <publishedDate>1997-02-28</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A polyhedral study of the asymmetric travelling salesman problem with time windows</title>
    <abstract language="eng">The asymmetric travelling salesman problem with time windows (ATSP-TW) is a basic model for scheduling and routing applications. In this paper we present a formulation of the problem involving only 0/1-variables associated with the arcs of the underlying digraph. This has the advantage of avoiding additional variables as well as the associated (typically very ineffective) linking constraints. In the formulation, time window restrictions are modelled by means of ``infeasible path elimination'' constraints. We present the basic form of these constraints along with some possible strengthenings. Several other classes of valid inequalities derived from related asymmetric travelling salesman problems are also described, along with a lifting theorem. We also study the ATSP-TW polytope, $P_{TW}$, defined as the convex hull of the integer solutions of our model. We show that determining the dimension of $P_{TW}$ is strongly {\em NP}--complete problem, even if only one time window is present. In this latter case, we provide a minimal equation system for $P_{TW}$. Computational experiments on the new formulation are reported in a companion paper [1997] where we show that it outperforms alternative formulations on some classes of problem instances.</abstract>
    <identifier type="serial">SC-97-11</identifier>
    <identifier type="opus3-id">281</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-2807</identifier>
    <enrichment key="SourceTitle">Appeared in: Networks 36 (2000) pp. 69-79</enrichment>
    <author>Norbert Ascheuer</author>
    <author>Matteo Fischetti</author>
    <author>Martin Grötschel</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-97-11</number>
    </series>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/280/SC-97-11.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/280/SC-97-11.pdf</file>
  </doc>
  <doc>
    <id>291</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1997-05-20</completedDate>
    <publishedDate>1997-05-20</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Cost-Efficient Network Synthesis from Leased Lines</title>
    <abstract language="eng">Given a communication demand between each pair of nodes of a network we consider the problem of deciding what capacity to install on each edge of the network in order to minimize the building cost of the network and to satisfy the demand between each pair of nodes. The feasible capacities that can be leased from a network provider are of a particular kind in our case. There are a few so-called basic capacities having the property that every basic capacity is an integral multiple of every smaller basic capacity. An edge can be equipped with a capacity only if it is an integer combination of the basic capacities. We treat, in addition, several restrictions on the routings of the demands (length restriction, diversification) and failures of single nodes or single edges. We formulate the problem as a mixed integer linear programming problem and develop a cutting plane algorithm as well as several heuristics to solve it. We report on computational results for real world data.</abstract>
    <identifier type="serial">SC-97-22</identifier>
    <identifier type="opus3-id">292</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-2912</identifier>
    <enrichment key="SourceTitle">Appeared in: Annals of Operations Research 76 (1998) 1-20</enrichment>
    <author>Dimitris Alevras</author>
    <author>Martin Grötschel</author>
    <author>Roland Wessäly</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-97-22</number>
    </series>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/291/SC-97-22.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/291/SC-97-22.pdf</file>
  </doc>
  <doc>
    <id>293</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1997-06-05</completedDate>
    <publishedDate>1997-06-05</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Capacity and Survivability Models for Telecommunication Networks</title>
    <abstract language="eng">Designing low-cost networks that survive certain failure situations is one of the prime tasks in the telecommunication industry. In this paper we survey the development of models for network survivability used in practice in the last ten years. We show how algorithms integrating polyhedral combinatorics, linear programming, and various heuristic ideas can help solve real-world network dimensioning instances to optimality or within reasonable quality guarantees in acceptable running times. The most general problem type we address is the following. Let a communication demand between each pair of nodes of a telecommunication network be given. We consider the problem of choosing, among a discrete set of possible capacities, which capacity to install on each of the possible edges of the network in order to (i) satisfy all demands, (ii) minimize the building cost of the network. \noindent In addition to determining the network topology and the edge capacities we have to provide, for each demand, a routing such that (iii) no path can carry more than a given percentage of the demand, (iv) no path in the routing exceeds a given length. \noindent We also have to make sure that (v) for every single node or edge failure, a certain percentage of the demand is reroutable. \noindent Moreover, for all failure situations feasible routings must be computed. The model described above has been developed in cooperation with a German mobile phone provider. We present a mixed-integer programming formulation of this model and computational results with data from practice.</abstract>
    <identifier type="serial">SC-97-24</identifier>
    <identifier type="opus3-id">294</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-2931</identifier>
    <enrichment key="SourceTitle">Appeared in: Proceedings of EURO XV/INFORMS XXXIV Meeting, Barcelona, Spain, 1997</enrichment>
    <author>Dimitris Alevras</author>
    <author>Martin Grötschel</author>
    <author>Roland Wessäly</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-97-24</number>
    </series>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/293/SC-97-24.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/293/SC-97-24.pdf</file>
  </doc>
  <doc>
    <id>294</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1997-06-13</completedDate>
    <publishedDate>1997-06-13</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Information Services for Mathematics in the Internet (Math-Net)</title>
    <abstract language="eng">The present paper gives a brief description of the Math-Net project which is carried out by nine mathematical institutions in Germany, supported by Deutsches Forschungsnetz (DFN) and Deutsche Telekom. The project aims at setting up the technical and organizational infrastructure for efficient, inexpensive and user-driven information services for mathematics. With the aid of active (structured retrieval mechanisms) and passive (profile services) components, electronic mathematical information in Germany will be made available to the scientist at his workplace. The emphasis is put on information about publications, software and data collections, teaching and research activities, but also on organizational and bibliographical information. Decentral organization structures, distributed search systems as well as the use of meta-information (metadata) in accordance with the Dublin Core (hopefully) guarantee a longterm, high-quality repository of data. The well-known mathematical software and data collection netlib\/ will be used as an example to illustrate how such a collection can be adapted to Math-Net. An integration of netlib into HyperWave offers additional perspectives and functionalities.</abstract>
    <identifier type="serial">SC-97-25</identifier>
    <identifier type="opus3-id">295</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-2949</identifier>
    <enrichment key="SourceTitle">Appeared in: Proc. of the 15th IMACS World Congress on Scientific Computation: Modelling and Applied Mathematics. A. Sydow (ed.) Wissenschaft und Technik Verlag, 1997, Vol. 4: Artificial Intelligence and Computer Science, pp. 773-778</enrichment>
    <author>Wolfgang Dalitz</author>
    <author>Martin Grötschel</author>
    <author>Joachim Lügger</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-97-25</number>
    </series>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/294/SC-97-25.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/294/SC-97-25.pdf</file>
  </doc>
  <doc>
    <id>251</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>deu</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1996-11-26</completedDate>
    <publishedDate>1996-11-26</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="deu">Kürzen muß nicht Kahlschlag heißen - das Beispiel Telebus-Behindertenfahrdienst Berlin</title>
    <abstract language="deu">Müssen Etatkürzungen bei staatlichen Dienstleistungseinrichtungen notwendig zu Leistungseinschränkungen oder Gebührenerhöhungen führen? Wir zeigen am Beispiel des Berliner Behindertenfahrdienstes {\em Telebus}, da\ss{} Sparzwang auch als Chance zur Verbesserung der eigenen Verwaltungs- und Arbeitsabläufe genutzt werden kann. Durch stärkere Dienstleistungsorientierung, Vereinfachung der Arbeitsabläufe und durch den Einsatz von moderner EDV und von mathematischen Optimierungsmethoden zur Fahrzeugeinsatzplanung werden bei Telebus heute staatliche Leistungen trotz geringeren Etats besser erbracht als vorher.</abstract>
    <identifier type="serial">SC-96-41</identifier>
    <identifier type="opus3-id">252</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-2510</identifier>
    <author>Ralf Borndörfer</author>
    <author>Martin Grötschel</author>
    <author>Werner Herzog</author>
    <author>Fridolin Klostermeier</author>
    <author>Wilhelm Konsek</author>
    <author>Christian Küttner</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-96-41</number>
    </series>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <collection role="projects" number="SenWiFo-Telebus">SenWiFo-Telebus</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/251/SC-96-41.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/251/SC-96-41.pdf</file>
  </doc>
  <doc>
    <id>258</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1996-12-02</completedDate>
    <publishedDate>1996-12-02</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Survivable Mobile Phone Architectures: Models and Solution Methods</title>
    <abstract language="eng">In the highly competitive area of telecommunications, cost, quality, and network management are among the most important aspects to be considered when designing a network. We study the problem of dimensioning a telecommunication network that is still operating in case of a failure of a network component. Given a demand between each pair of nodes of a telecommunication network and a finite set of possible capacities for each edge of the network, we consider the problem of deciding what capacity to install on each edge of the network in order to minimize the building cost of the network and to satisfy the demand between each pair of nodes, even if a network component fails. The routing of the demands must satisfy the following additional restrictions: (a) there is a maximum number of nodes allowed in each path between any pair of nodes (path length restriction), and (b) there is a maximum percentage of the demand between each pair of nodes that can be routed through any network component (diversification restriction). Moreover, the chosen capacities must be such that, for every single node or single edge failure, a certain percentage of the demand between any pair of nodes is reroutable (i.e. it ``survives'' the particular failure). We formulate the problem as a mixed integer linear programming problem and present a cutting plane algorithm as well as several heuristics for its solution. Furthermore, we discuss several ways to implement survivability into a telecommunication network.</abstract>
    <identifier type="serial">SC-96-48</identifier>
    <identifier type="opus3-id">259</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-2582</identifier>
    <enrichment key="SourceTitle">Appeared in: IEEE Communications Magazine 36 (1998) 88-93</enrichment>
    <author>Dimitris Alevras</author>
    <author>Martin Grötschel</author>
    <author>Peter Jonas</author>
    <author>Ulrich Paul</author>
    <author>Roland Wessäly</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-96-48</number>
    </series>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/258/SC-96-48.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/258/SC-96-48.pdf</file>
  </doc>
  <doc>
    <id>259</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1996-12-02</completedDate>
    <publishedDate>1996-12-02</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Network Dimensioning Tool</title>
    <abstract language="eng">Designing low cost networks that survive certain failure situations belongs to one of the prime tasks in the telecommunications industry. In this paper we describe a mathematical model combining several aspects of survivability that are elsewhere treated in a hierarchical fashion. We present mathematical investigations of this integrated model, a cutting plane algorithm, as well as several heuristics for its solution. Moreover, we report computational results with real world data. The problem we address is the following. Suppose, between each pair of nodes in a region, a communication demand is given. We want to determine the topology of a telecommunication network connecting the given nodes and to dimension all potential physical links. For each link, the possible capacities are restricted to a given finite set. The capacities must be chosen such that the communication demands are satisfied, even if certain network components fail, and such that the network building costs are as small as possible. Moreover, for each pair of nodes and each failure situation, we want to determine the paths on which the demand between the nodes is routed.</abstract>
    <identifier type="serial">SC-96-49</identifier>
    <identifier type="opus3-id">260</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-2591</identifier>
    <author>Dimitris Alevras</author>
    <author>Martin Grötschel</author>
    <author>Roland Wessäly</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-96-49</number>
    </series>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/259/SC-96-49.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/259/SC-96-49.pdf</file>
  </doc>
  <doc>
    <id>250</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>deu</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1996-11-26</completedDate>
    <publishedDate>1996-11-26</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="deu">Telebus Berlin - Mobilität für Behinderte</title>
    <abstract language="deu">Steigendes Mobilitätsbedürfnis der Behinderten bei angespannter Haushaltslage --- diese Situation ergab vor drei Jahren beim Berliner Behindertenfahrdienst {\em Telebus\/} Handlungsbedarf. Gleichzeitig stie\ss{} die verwendete manuelle (Fahrzeug-)Tourenplanung mit damals etwa 1.000 Fahrtwünschen pro Tag an ihre Grenzen. Zur Lösung dieser Probleme war der effiziente Einsatz von Computern und von {\em mathematischen Optimierungsverfahren\/} erforderlich. Ergebnis des daraufhin gestarteten {\em Telebus-Projektes\/} ist die Entwicklung eines neuen, alle Arbeitsabläufe unterstützenden Computersystems, das seit über einem Jahr im Einsatz ist. Herzstück dieses Systems ist ein auf mathematischen Methoden der ganzzahligen Optimierung basierendes Verfahren zur Tourenplanung. Ziel dieses Artikels ist die Beschreibung dieses Verfahrens und seiner Verwendung bei der Behindertenbeförderung. Das Beispiel Telebus zeigt, da\ss{} der Einsatz mathematischer Optimierungstechniken neue Möglichkeiten für Kosteneinsparungen bei gleichzeitiger Serviceverbesserung auch in anderen Bereichen des ÖPNV eröffnet.</abstract>
    <identifier type="serial">SC-96-40</identifier>
    <identifier type="opus3-id">251</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-2500</identifier>
    <enrichment key="SourceTitle">Erschienen unter dem Titel: "Berliner Telebussystem bietet Mobilität für Behinderte" in: Der Nahverkehr (1-2) 20-22 (1997)</enrichment>
    <author>Ralf Borndörfer</author>
    <author>Martin Grötschel</author>
    <author>Fridolin Klostermeier</author>
    <author>Christian Küttner</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-96-40</number>
    </series>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="institutes" number="traffic">Mathematics of Transportation and Logistics</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <collection role="projects" number="SenWiFo-Telebus">SenWiFo-Telebus</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/250/SC-96-40.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/250/SC-96-40.pdf</file>
  </doc>
  <doc>
    <id>197</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
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    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1995-11-29</completedDate>
    <publishedDate>1995-11-29</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Optimum Path Packing on Wheels: The Consecutive Case</title>
    <abstract language="eng">We show that, given a wheel with nonnegative edge lengths and pairs of terminals located on the wheel's outer cycle such that the terminal pairs are in consecutive order, then a path packing, i.~e., a collection of edge disjoint paths connecting the given terminal pairs, of minimum length can be found in strongly polynomial time. Moreover, we exhibit for this case a system of linear inequalities that provides a complete and nonredundant description of the path packing polytope, which is the convex hull of all incidence vectors of path packings and their supersets.</abstract>
    <identifier type="serial">SC-95-31</identifier>
    <identifier type="opus3-id">197</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-1976</identifier>
    <enrichment key="SourceTitle">Appeared in: Computers Math. Applic., Vol. 31, No. 11, pp. 23-35, 1996</enrichment>
    <author>Martin Grötschel</author>
    <author>Alexander Martin</author>
    <author>Robert Weismantel</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-95-31</number>
    </series>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/197/SC-95-31.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/197/SC-95-31.pdf</file>
  </doc>
  <doc>
    <id>170</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>deu</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1995-02-07</completedDate>
    <publishedDate>1995-02-07</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="deu">Simulation und Optimierung einer PC-Fertigung unter Echtzeitbedingungen</title>
    <abstract language="deu">Die Business Unit PC in Augsburg ist die zentrale Produktionsstätte der Siemens--Nixdorf Informationssysteme (SNI) AG für Personal Computer sowie für einige Periphärgeräte. Das Werk, entworfen nach modernen CIM/CAI--Konzepten (Computer Integrated Manufacturing/ Computer Aided Industry), wurde 1987 errichtet. Bald zeigte sich jedoch, daß es für ein zu geringes Produktionsvolumen ausgelegt war und einige Komponenten des Systems Engpässe im Produktionsbetrieb darstellen. Das Management suchte nach Möglichkeiten, den Produktionsfluß zu verbessern, ohne teure technische Änderungen am System vornehmen zu müssen. Eine Forschungsgruppe des Konrad--Zuse--Zentrums für Informationstechnik (die ehemals an der Universität Augsburg ansässig war) analysierte, unterstützt von einigen Studenten und Ingenieuren der SNI, den Produktionsfluß und lokalisierte Schwachstellen. Basierend auf diesen Erkenntnissen wurden mathematische Fragestellungen erarbeitet und auf mathematischen Optimierungsverfahren basierende Softwarepakete entwickelt, die jetzt teilweise bei SNI im Einsatz sind. Im folgenden werden einige dieser Fragestellungen, deren Modellierung und mathematische Behandlung beschrieben. Einige der Ansätze, die hier dargestellt werden sollen, sind teilweise schon in Grötschel [Grö92] angesprochen worden.</abstract>
    <identifier type="serial">SC-95-04</identifier>
    <identifier type="opus3-id">170</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-1700</identifier>
    <enrichment key="SourceTitle">Appeared in: Mathematik in der Praxis : Fallstudien aus Industrie, Wirtschaft, Naturwissenschaft und Medizin. A. Bachem (ed.) Springer 1995, pp. 261-277</enrichment>
    <author>Atef Abdel-Aziz Abdel-Hamid</author>
    <author>Norbert Ascheuer</author>
    <author>Martin Grötschel</author>
    <author>Herbert Schorer</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-95-04</number>
    </series>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/170/SC-95-04.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/170/SC-95-04.pdf</file>
  </doc>
  <doc>
    <id>132</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
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    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1994-01-20</completedDate>
    <publishedDate>1994-01-20</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">The Steiner Tree Packing Problem in VLSI-Design.</title>
    <abstract language="eng">In this paper we describe several versions of the routing problem arising in VLSI design and indicate how the Steiner tree packing problem can be used to model these problems mathematically. We focus on switchbox routing problems and provide integer programming formulations for routing in the knock-knee and in the Manhattan model. We give a brief sketch of cutting plane algorithms that we developed and implemented for these two models. We report on computational experiments using standard test instances. Our codes are able to determine optimum solutions in most cases, and in particular, we can show that some of the instances have no feasible solution if Manhattan routing is used instead of knock-knee routing.</abstract>
    <identifier type="serial">SC-94-02</identifier>
    <identifier type="opus3-id">132</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-1328</identifier>
    <enrichment key="SourceTitle">Appeared in: Mathematical Programming 78 (1997) 265-281</enrichment>
    <author>Martin Grötschel</author>
    <author>Alexander Martin</author>
    <author>Robert Weismantel</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-94-02</number>
    </series>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/132/SC-94-02.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/132/SC-94-02.pdf</file>
  </doc>
  <doc>
    <id>122</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1993-10-27</completedDate>
    <publishedDate>1993-10-27</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Optimum Path Packing on Wheels: The Noncrossing Case.</title>
    <abstract language="eng">We show that, given a wheel with nonnegative edge lengths and pairs of terminals located on the wheel's outer cycle such that no two terminal pairs cross, then a path packing, i.~e.,a collection of edge disjoint paths connecting the given terminal pairs, of minimum length can be found in strongly polynomial time. Moreover, we exhibit for this case a system of linear inequalities that provides a complete and nonredundant description of the path packing polytope, which is the convex hull of all incidence vectors of path packings and their supersets.</abstract>
    <identifier type="serial">SC-93-26</identifier>
    <identifier type="opus3-id">121</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-1225</identifier>
    <enrichment key="SourceTitle">See SC 95-31 for an updated version</enrichment>
    <author>Martin Grötschel</author>
    <author>Alexander Martin</author>
    <author>Robert Weismantel</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-93-26</number>
    </series>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/122/SC-93-26.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/122/SC-93-26.pdf</file>
  </doc>
  <doc>
    <id>129</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1994-01-19</completedDate>
    <publishedDate>1994-01-19</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Ulysses 2000: In Search of Optimal Solutions to Hard Combinatorial Problems.</title>
    <abstract language="eng">Combinatorial optimization problems pervade many areas of human problem solving especially in the fields of business, economics and engineering. Intensive mathematical research and vast increases in raw computing power have advanced the state of the art in exact and heuristic problem solving at a pace that is unprecedented in human history. We survey here in layman's terms some of the fundamental concepts and principles that have led this progress. (This article will appear -- possibly in modified form -- in a popular science magazine.)</abstract>
    <identifier type="serial">SC-93-34</identifier>
    <identifier type="opus3-id">129</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-1296</identifier>
    <enrichment key="SourceTitle">A revised German version appeared under the title: &lt;a href="http://www.spektrum.de/odyssee.html"&gt; Die optimierte Odyssee &lt;/a&gt;, In: Spektrum der Wissenschaft, 4/1999, 11-13</enrichment>
    <author>Martin Grötschel</author>
    <author>Manfred Padberg</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-93-34</number>
    </series>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/129/SC-93-34.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/129/SC-93-34.ps</file>
  </doc>
  <doc>
    <id>105</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1993-03-22</completedDate>
    <publishedDate>1993-03-22</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Design of Survivable Networks</title>
    <identifier type="serial">SC-93-09</identifier>
    <identifier type="opus3-id">104</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-1054</identifier>
    <enrichment key="SourceTitle">Appeared in: Handbooks in Operations Research and Management Science. Vol. 7: Network Models. M. O. Ball et al. (eds.) Elsevier 1995. Chapter 10, pp. 617-672</enrichment>
    <author>Martin Grötschel</author>
    <author>Clyde Monma</author>
    <author>Mechthild Stoer</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-93-09</number>
    </series>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/105/SC-93-09.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/105/SC-93-09.pdf</file>
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  <doc>
    <id>109</id>
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    <language>eng</language>
    <pageFirst/>
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    <pageNumber/>
    <edition/>
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    <completedDate>1993-06-24</completedDate>
    <publishedDate>1993-06-24</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Combinatorial Optimization.</title>
    <abstract language="eng">This paper will appear as Chapter 28 of the forthcoming "Handbook on Combinatorics" (editors: R. Graham, M. Grötschel, L. Lovasz) to be published in 1994, by North-Holland.</abstract>
    <identifier type="serial">SC-93-13</identifier>
    <identifier type="opus3-id">108</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-1098</identifier>
    <enrichment key="SourceTitle">Appeared in: Handbooks of Combinatorics. Ed. by R. L. Graham, M. Grötschel, L. Lovasz. Vol. II. Elsevier; MIT Press 1995, pp. 1541-1597</enrichment>
    <author>Martin Grötschel</author>
    <author>Lászlo Lovász</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-93-13</number>
    </series>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/109/SC-93-13.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/109/SC-93-13.pdf</file>
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  <doc>
    <id>69</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1992-01-06</completedDate>
    <publishedDate>1992-01-06</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Combinatorics in Statistical Physics</title>
    <identifier type="serial">SC-91-19</identifier>
    <identifier type="opus3-id">68</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-694</identifier>
    <enrichment key="SourceTitle">Appeared in: Handbooks of Combinatorics. Ed. by R. L. Graham, M. Grötschel, L. Lovasz. Vol. II. Elsevier; MIT Press 1995, pp. 1925-1954</enrichment>
    <author>C. D. Godsil</author>
    <author>Martin Grötschel</author>
    <author>D. J. A. Welsh</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-91-19</number>
    </series>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/69/SC-91-19.pdf</file>
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  <doc>
    <id>73</id>
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    <language>eng</language>
    <pageFirst/>
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    <pageNumber/>
    <edition/>
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    <type>reportzib</type>
    <publisherName/>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1992-03-23</completedDate>
    <publishedDate>1992-03-23</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Discrete Mathematics in Manufacturing.</title>
    <abstract language="eng">Manufacturing is a topic that provides rich opportunities for important mathematical contributions to real-world problems. The purpose of this paper is to show, by means of several examples, where and how mathematical problems of a discrete nature arise in manufacturing and to demonstrate the savings and improvements that can be achieved by employing the techniques of combinatorial optimization. The topics covered range from the design phase of a product (e. g.,routing, placement and via minimization in VLSI design), the control of CNC machines (e. g., drilling and plotting), to the management of assembly lines, storage systems and whole factories. We also point out difficulties in the modelling of complex situations and outline the algorithmic methods that are used for the solution of the mathematical problems arising in manufacturing. {\bf Key words:} discrete mathematics , combinatorial optimization, applications to manufacturing.</abstract>
    <identifier type="serial">SC-92-03</identifier>
    <identifier type="opus3-id">72</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-738</identifier>
    <enrichment key="SourceTitle">Appeared in: Robert E. O'Malley (ed.) ICIAM 1991. Proc. of the Second Int. Conf. on Industrial and Applied Mathematics, SIAM, 1991, pp. 119-145</enrichment>
    <author>Martin Grötschel</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-92-03</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>discrete mathematics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>combinatorial optimization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>applications to manufacturing</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/73/SC-92-03.pdf</file>
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  <doc>
    <id>78</id>
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    <language>eng</language>
    <pageFirst/>
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    <pageNumber/>
    <edition/>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1992-04-09</completedDate>
    <publishedDate>1992-04-09</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Packing Steiner Trees: Polyhedral Investigations.</title>
    <abstract language="eng">Let $G=(V,E)$ be a graph and $T\subseteq V$ be a node set. We call an edge set $S$ a Steiner tree with respect to $T$ if $S$ connects all pairs of nodes in $T$. In this paper we address the following problem, which we call the weighted Steiner tree packing problem. Given a graph $G=(V,E)$ with edge weights $w_e$, edge capacities $c_e, e \in E,$ and node sets $T_1,\ldots,T_N$, find edge sets $S_1,\ldots,S_N$ such that each $S_k$ is a Steiner tree with respect to $T_k$, at most $c_e$ of these edge sets use edge $e$ for each $e\in E$, and such that the sum of the weights of the edge sets is minimal. Our motivation for studying this problem arises from the routing problem in VLSI-design, where given sets of points have to be connected by wires. We consider the Steiner tree packing Problem from a polyhedral point of view and define an appropriate polyhedron, called the Steiner tree packing polyhedron. The goal of this paper is to (partially) describe this polyhedron by means of inequalities. It turns out that, under mild assumptions, each inequality that defines a facet for the (single) Steiner tree polyhedron can be lifted to a facet-defining inequality for the Steiner tree packing polyhedron. The main emphasis of this paper lies on the presentation of so-called joint inequalities that are valid and facet-defining for this polyhedron. Inequalities of this kind involve at least two Steiner trees. The classes of inequalities we have found form the basis of a branch &amp; cut algorithm. This algorithm is described in our companion paper SC 92-09.</abstract>
    <identifier type="serial">SC-92-08</identifier>
    <identifier type="opus3-id">77</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-786</identifier>
    <identifier type="doi">10.1007/BF02592085</identifier>
    <enrichment key="SourceTitle">Appeared in: Mathematical Programming 72 (1996) 101-123</enrichment>
    <author>Martin Grötschel</author>
    <author>Alexander Martin</author>
    <author>Robert Weismantel</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-92-08</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>cutting planes</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Facets</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Packing</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>polyhedron</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Steiner tree</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/78/SC-92-08.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/78/SC-92-08.pdf</file>
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