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    <id>197</id>
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    <language>eng</language>
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    <pageNumber/>
    <edition/>
    <issue/>
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    <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>132</id>
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    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
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    <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/>
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    <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>78</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
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    <contributingCorporation/>
    <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>
  </doc>
  <doc>
    <id>79</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1992-04-09</completedDate>
    <publishedDate>1992-04-09</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Packing Steiners Trees: A Cutting Plane Algorithm and Computational Results.</title>
    <abstract language="eng">In this paper we describe a cutting plane algorithm for the Steiner tree packing problem. We use our algorithm to solve some switchbox routing problems of VLSI-design and report on our computational experience. This includes a brief discussion of separation algorithms, a new LP-based primal heuristic and implementation details. The paper is based on the polyhedral theory for the Steiner tree packing polyhedron developed in our companion paper SC 92-8 and meant to turn this theory into an algorithmic tool for the solution of practical problems.</abstract>
    <identifier type="serial">SC-92-09</identifier>
    <identifier type="opus3-id">78</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-792</identifier>
    <enrichment key="SourceTitle">Appeared in: Mathematical Programming 72 (1996) 125-145</enrichment>
    <author>Martin Grötschel</author>
    <author>Alexander Martin</author>
    <author>Robert Weismantel</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-92-09</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/79/SC-92-09.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/79/SC-92-09.pdf</file>
  </doc>
  <doc>
    <id>95</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1993-01-13</completedDate>
    <publishedDate>1993-01-13</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Some Integer Programs Arising in the Design of Main Frame Computers.</title>
    <abstract language="eng">In this paper we describe and discuss a problem that arises in the (global) design of a main frame computer. The task is to assign certain functional units to a given number of so called multi chip modules or printed circuit boards taking into account many technical constraints and minimizing a complex objective function. We describe the real world problem. A thorough mathematical modelling of all aspects of this problem results in a rather complicated integer program that seems to be hopelessly difficult -- at least for the present state of integer programming technology. We introduce several relaxations of the general model, which are also $NP$-hard, but seem to be more easily accessible. The mathematical relations between the relaxations and the exact formulation of the problem are discussed as well.</abstract>
    <identifier type="serial">SC-92-25</identifier>
    <identifier type="opus3-id">94</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-957</identifier>
    <enrichment key="SourceTitle">Appeared in: Zeitschrift für Operations Research 38 1 (1993) pp. 77-100.</enrichment>
    <author>Carlos E. Ferreira</author>
    <author>Martin Grötschel</author>
    <author>Stefan Kiefl</author>
    <author>Ludwig Krispenz</author>
    <author>Alexander Martin</author>
    <author>Robert Weismantel</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-92-25</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/95/SC-92-25.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/95/SC-92-25.pdf</file>
  </doc>
  <doc>
    <id>96</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1992-12-02</completedDate>
    <publishedDate>1992-12-02</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Routing in Grid Graphs by Cutting Planes.</title>
    <abstract language="eng">{\def\N{{\cal N}} \def\R{\hbox{\rm I\kern-2pt R}} \def\MN{{\rm I\kern-2pt N}} In this paper we study the following problem, which we call the weighted routing problem. Let be given a graph $G=(V,E)$ with non-negative edge weights $w_e\in\R_+$ and integer edge capacities $c_e\in\MN$ and let $\N=\{T_1,\ldots,T_N\}$, $N\ge 1$, be a list of node sets. The weighted routing problem consists in finding edge sets $S_1,\ldots,S_N$ such that, for each $k\in\{1,\ldots,N\}$, the subgraph $(V(S_k),S_k)$ contains an $[s,t]$-path for all $s,t\in T_k$, 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 weighted routing problem from a polyhedral point of view. We define an appropriate polyhedron and try to (partially) describe this polyhedron by means of inequalities. We briefly sketch our separation algorithms for some of the presented classes of inequalities. Based on these separation routines we have implemented a branch and cut algorithm. Our algorithm is applicable to an important subclass of routing problems arising in VLSI-design, namely to problems where the underlying graph is a grid graph and the list of node sets is located on the outer face of the grid. We report on our computational experience with this class of problem instances.}</abstract>
    <identifier type="serial">SC-92-26</identifier>
    <identifier type="opus3-id">95</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-967</identifier>
    <enrichment key="SourceTitle">Appeared in: Integer Programming and Combinatorial Optimization - IPCO-03. Proc. of a Conf., Erice, April 29 - May 1, 1993. Core, Louvain-la-Neuve, Belgium, 1993, pp. 447-461. An extended version appeared in: ZOR - Mathematical Methods of Operations Research 41 (1995) pp. 255-275</enrichment>
    <author>Martin Grötschel</author>
    <author>Alexander Martin</author>
    <author>Robert Weismantel</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-92-26</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>routing in VLSI-design</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Steiner tree</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Steiner tree packing</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>cutting plane algorithm</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/96/SC-92-26.pdf</file>
  </doc>
  <doc>
    <id>97</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1992-12-02</completedDate>
    <publishedDate>1992-12-02</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Packing Steiner Trees: Further Facets.</title>
    <abstract language="eng">In this paper we continue the investigations in [GMW92a] for the \def\sbppo{Steiner tree packing polyhedron} \sbppo. We present several new classes of valid inequalities and give sufficient (and necessary) conditions for these inequalities to be facet-defining. It is intended to incorporate these inequalities into an existing cutting plane algorithm that is applicable to practical problems arising in the design of electronic circuits.</abstract>
    <identifier type="serial">SC-93-01</identifier>
    <identifier type="opus3-id">96</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-975</identifier>
    <identifier type="doi">10.1006/eujc.1996.0004</identifier>
    <enrichment key="SourceTitle">Appeared in: Europ. J. Combinatorics (1996) 17, 39-52</enrichment>
    <author>Martin Grötschel</author>
    <author>Alexander Martin</author>
    <author>Robert Weismantel</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-93-01</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/97/SC-93-01.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/97/SC-93-01.pdf</file>
  </doc>
  <doc>
    <id>98</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1992-12-02</completedDate>
    <publishedDate>1992-12-02</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Packing Steiner Trees: Separation Algorithms.</title>
    <abstract language="eng">In this paper we investigate separation problems for classes of inequalities valid for the polytope associated with the Steiner tree packing problem, a problem that arises, e.~g., in VLSI routing. The separation problem for Steiner partition inequalities is ${\cal N}\hskip-2pt{\cal P}$-hard in general. We show that it can be solved in polynomial time for those instances that come up in switchbox routing. Our algorithm uses dynamic programming techniques. These techniques are also applied to the much more complicated separation problem for alternating cycle inequalities. In this case we can compute in polynomial time, given some point $y$, a lower bound for the gap $\alpha-a^Ty$ over all alternating cycle inequalities $a^Tx\ge\alpha$. This gives rise to a very effective separation heuristic. A by-product of our algorithm is the solution of a combinatorial optimization problem that is interesting in its own right: Find a shortest path in a graph where the ``length'' of a path is its usual length minus the length of its longest edge.</abstract>
    <identifier type="serial">SC-93-02</identifier>
    <identifier type="opus3-id">97</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-984</identifier>
    <identifier type="doi">10.1137/S0895480193258716</identifier>
    <enrichment key="SourceTitle">Appeared in: SIAM J. Discrete Math. 9 (1996) pp. 233-257</enrichment>
    <author>Martin Grötschel</author>
    <author>Alexander Martin</author>
    <author>Robert Weismantel</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-93-02</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/98/SC-93-02.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/98/SC-93-02.pdf</file>
  </doc>
  <doc>
    <id>304</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1997-07-11</completedDate>
    <publishedDate>1997-07-11</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Frequency Assignment in Cellular Phone Networks</title>
    <abstract language="eng">We present a graph-theoretic model for the \emph{frequency assignment problem} in Cellular Phone Networks: Obeying several technical and legal restrictions, frequencies have to be assigned to transceivers so that interference is as small as possible. This optimization problem is NP-hard. Good approximation cannot be guaranteed, unless P = NP. We describe several assignment heuristics. These heuristics are simple and not too hard to implement. We give an assessment of the heuristics' efficiency and practical usefulness. For this purpose, typical instances of frequency assignment problems with up to 4240 transceivers and 75 frequencies of a German cellular phone network operator are used. The results are satisfying from a practitioner's point of view. The best performing heuristics were integrated into a network planning system used in practice.</abstract>
    <identifier type="serial">SC-97-35</identifier>
    <identifier type="opus3-id">305</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-3044</identifier>
    <identifier type="doi">10.1023/A:1018908907763</identifier>
    <enrichment key="SourceTitle">Appeared in: Annals of OR 76 (1998), 73-93</enrichment>
    <author>Ralf Borndörfer</author>
    <author>Andreas Eisenblätter</author>
    <author>Martin Grötschel</author>
    <author>Alexander Martin</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-97-35</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>
    <file>https://opus4.kobv.de/opus4-zib/files/304/SC-97-35.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/304/SC-97-35.pdf</file>
  </doc>
  <doc>
    <id>562</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
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    <completedDate>1998-04-03</completedDate>
    <publishedDate>1998-04-03</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">The Orientation Model for Frequency Assignment Problems</title>
    <abstract language="eng">Mobile telecommunication systems establish a large number of communication links with a limited number of available frequencies; reuse of the same or adjacent frequencies on neighboring links causes interference. The task to find an assignment of frequencies to channels with minimal interference is the frequency assignment problem. The frequency assignment problem is usually treated as a graph coloring problem where the number of colors is minimized, but this approach does not model interference minimization correctly. We give in this paper a new integer programming formulation of the frequency assignment problem, the orientation model, and develop a heuristic two-stage method to solve it. The algorithm iteratively solves an outer and an inner optimization problem. The outer problem decides for each pair of communication links which link gets the higher frequency and leads to an acyclic subdigraph problem with additional longest path restrictions. The inner problem to find an optimal assignment respecting an orientation leads to a min-cost flow problem.</abstract>
    <identifier type="serial">TR-98-01</identifier>
    <identifier type="opus3-id">563</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-5627</identifier>
    <author>Ralf Borndörfer</author>
    <author>Andreas Eisenblätter</author>
    <author>Martin Grötschel</author>
    <author>Alexander Martin</author>
    <series>
      <title>ZIB-Report</title>
      <number>TR-98-01</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Minimum-Cost Flow Problems</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Cellular Radio Telephone Systems</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Frequency Assignment Problem</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Integer Programming</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="90B10">Network models, deterministic</collection>
    <collection role="msc" number="90B80">Discrete location and assignment [See also 90C10]</collection>
    <collection role="msc" number="90C10">Integer programming</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="eplus-FAP">eplus-FAP</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/562/TR-98-01.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/562/TR-98-01.pdf</file>
  </doc>
  <doc>
    <id>3105</id>
    <completedYear>1996</completedYear>
    <publishedYear>1996</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>101</pageFirst>
    <pageLast>123</pageLast>
    <pageNumber/>
    <edition/>
    <issue>2</issue>
    <volume>72</volume>
    <type>article</type>
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    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Packing Steiner trees: Polyhedral Investigations</title>
    <parentTitle language="eng">Mathematical Programming, Series A</parentTitle>
    <identifier type="doi">10.1007/BF02592085</identifier>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-786</enrichment>
    <author>Martin Grötschel</author>
    <author>Alexander Martin</author>
    <author>Robert Weismantel</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>3104</id>
    <completedYear>1996</completedYear>
    <publishedYear>1996</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>23</pageFirst>
    <pageLast>35</pageLast>
    <pageNumber/>
    <edition/>
    <issue>11</issue>
    <volume>31</volume>
    <type>article</type>
    <publisherName>Elsevier</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Optimum Path Packing on Wheels</title>
    <parentTitle language="eng">Computers and Mathematics with Applications</parentTitle>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-1976</enrichment>
    <author>Martin Grötschel</author>
    <author>Alexander Martin</author>
    <author>Robert Weismantel</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>3118</id>
    <completedYear>1998</completedYear>
    <publishedYear>1998</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>73</pageFirst>
    <pageLast>93</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>76</volume>
    <type>article</type>
    <publisherName>J. C. Baltzer AG, Science Publishers</publisherName>
    <publisherPlace/>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Frequency assignment in cellular phone networks</title>
    <parentTitle language="eng">Annals of Operations Research</parentTitle>
    <identifier type="doi">10.1023/A:1018908907763</identifier>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-3044</enrichment>
    <author>Ralf Borndörfer</author>
    <author>Andreas Eisenblätter</author>
    <author>Martin Grötschel</author>
    <author>Alexander Martin</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <collection role="projects" number="eplus-FAP">eplus-FAP</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>3106</id>
    <completedYear>1996</completedYear>
    <publishedYear>1996</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>125</pageFirst>
    <pageLast>145</pageLast>
    <pageNumber/>
    <edition/>
    <issue>2</issue>
    <volume>72</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Packing Steiner trees: a cutting plane algorithm and computational results</title>
    <parentTitle language="eng">Mathematical Programming, Series A</parentTitle>
    <identifier type="doi">10.1007/BF02592086</identifier>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-792</enrichment>
    <author>Martin Grötschel</author>
    <author>Alexander Martin</author>
    <author>Robert Weismantel</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>3114</id>
    <completedYear>1997</completedYear>
    <publishedYear>1997</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>265</pageFirst>
    <pageLast>281</pageLast>
    <pageNumber/>
    <edition/>
    <issue>2</issue>
    <volume>78</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">The Steiner tree packing problem in VLSI design</title>
    <parentTitle language="eng">Mathematical Programming</parentTitle>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-1328</enrichment>
    <author>Martin Grötschel</author>
    <author>Alexander Martin</author>
    <author>Robert Weismantel</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>3079</id>
    <completedYear>1993</completedYear>
    <publishedYear>1993</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>447</pageFirst>
    <pageLast>461</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName>Librarian CORE</publisherName>
    <publisherPlace>Louvain-la-Neuve</publisherPlace>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Routing in grid graphs by cutting planes</title>
    <parentTitle language="eng">Integer Programming and Combinatorial Optimization. Proceedings of a Conference held at Centro Ettore Majorana, Erice, Italy, April 29 - May 1, 1993</parentTitle>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-967</enrichment>
    <author>Martin Grötschel</author>
    <editor>Giovanni Rinaldi</editor>
    <author>Alexander Martin</author>
    <editor>Laurence Wolsey</editor>
    <author>Robert Weismantel</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>3076</id>
    <completedYear>1993</completedYear>
    <publishedYear>1993</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>77</pageFirst>
    <pageLast>100</pageLast>
    <pageNumber/>
    <edition/>
    <issue>1</issue>
    <volume>38</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Some Integer Programs Arising in the Design of Main Frame Computers</title>
    <parentTitle language="eng">ZOR - Methods and Models of Operations Research</parentTitle>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-957</enrichment>
    <author>Carlos Ferreira</author>
    <author>Martin Grötschel</author>
    <author>Alexander Martin</author>
    <author>Robert Weismantel</author>
    <author>Stefan Kiefl</author>
    <author>Ludwig Krispenz</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>3096</id>
    <completedYear>1995</completedYear>
    <publishedYear>1995</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>255</pageFirst>
    <pageLast>275</pageLast>
    <pageNumber/>
    <edition/>
    <issue>3</issue>
    <volume>41</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Routing in Grid Graphs by Cutting Planes</title>
    <parentTitle language="eng">ZOR - Mathematical Methods of Operations Research</parentTitle>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-967</enrichment>
    <author>Martin Grötschel</author>
    <author>Alexander Martin</author>
    <author>Robert Weismantel</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>3103</id>
    <completedYear>1996</completedYear>
    <publishedYear>1996</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>233</pageFirst>
    <pageLast>257</pageLast>
    <pageNumber/>
    <edition/>
    <issue>2</issue>
    <volume>9</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Packing Steiner Trees: Separation Algorithms</title>
    <parentTitle language="eng">SIAM Journal on Discrete Mathematics</parentTitle>
    <identifier type="doi">10.1137/S0895480193258716</identifier>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-984</enrichment>
    <author>Martin Grötschel</author>
    <author>Alexander Martin</author>
    <author>Robert Weismantel</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>3102</id>
    <completedYear>1996</completedYear>
    <publishedYear>1996</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>39</pageFirst>
    <pageLast>52</pageLast>
    <pageNumber/>
    <edition/>
    <issue>1</issue>
    <volume>17</volume>
    <type>article</type>
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    <creatingCorporation/>
    <contributingCorporation/>
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    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Packing Steiner Trees: Further Facets</title>
    <parentTitle language="eng">European Journal of Combinatorics</parentTitle>
    <identifier type="doi">10.1006/eujc.1996.0004</identifier>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-975</enrichment>
    <author>Martin Grötschel</author>
    <author>Alexander Martin</author>
    <author>Robert Weismantel</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>2836</id>
    <completedYear>1996</completedYear>
    <publishedYear>1996</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>17</pageFirst>
    <pageLast>21</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName>Universidade de São Paulo, Instituto de Matemática e Estatística</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Stable-Set and Other Techniques for Frequency Assignment Problems</title>
    <parentTitle language="eng">Anais da I Oficina Nacional em Problemas de Corte &amp; Empacotamento</parentTitle>
    <author>Ralf Borndörfer</author>
    <author>Andreas Eisenblätter</author>
    <author>Martin Grötschel</author>
    <author>Alexander Martin</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <collection role="projects" number="eplus-FAP">eplus-FAP</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>3056</id>
    <completedYear>1988</completedYear>
    <publishedYear>1988</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>2</volume>
    <type>book</type>
    <publisherName>Springer</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <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>
  </doc>
  <doc>
    <id>3035</id>
    <completedYear>1984</completedYear>
    <publishedYear>1984</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>167</pageFirst>
    <pageLast>183</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName>Academic Press</publisherName>
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    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <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>
    <author>Alexander Schrijver</author>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
  </doc>
  <doc>
    <id>3036</id>
    <completedYear>1984</completedYear>
    <publishedYear>1984</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>325</pageFirst>
    <pageLast>356</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>21</volume>
    <type>bookpart</type>
    <publisherName>North-Holland</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <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/>
    <publisherPlace/>
    <creatingCorporation/>
    <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>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>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>
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    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
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    <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>
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    <id>3077</id>
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    <language>eng</language>
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    <pageNumber/>
    <edition>Second corrected edition</edition>
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    <volume>2</volume>
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    <title language="eng">Geometric Algorithms and Combinatorial Optimization</title>
    <parentTitle language="eng">Algorithms and Combinatorics</parentTitle>
    <identifier type="isbn">3-540-56740-2, 0-387-56740-2 (U.S.)</identifier>
    <author>Martin Grötschel</author>
    <author>Lászlo Lovász</author>
    <author>Alexander Schrijver</author>
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    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
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</export-example>
