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  <doc>
    <id>394</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
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    <completedDate>1999-03-03</completedDate>
    <publishedDate>1999-03-03</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Euler is Standing in Line</title>
    <abstract language="eng">In this paper we study algorithms for ``Dial-a-Ride'' transportation problems. In the basic version of the problem we are given transportation jobs between the vertices of a graph and the goal is to find a shortest transportation that serves all the jobs. This problem is known to be NP-hard even on trees. We consider the extension when precedence relations between the jobs with the same source are given. Our results include a polynomial time algorithm on paths and an approximation algorithm on general graphs with a performance of~$9/4$. For trees we improve the performance to~$5/3$.</abstract>
    <identifier type="serial">SC-99-06</identifier>
    <identifier type="opus3-id">395</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-3947</identifier>
    <enrichment key="SourceTitle">Appeared in: Discrete Appl. Math. 113 (2001) 87-107. A prel. vers. appeared in: Proc. of the 25nd Intern. Workshop on Graph-Theoretic Concepts in Computer Science (WG'99), Lecture Notes in Computer Science, vol. 1665, Springer (1999) 42-54</enrichment>
    <author>Dietrich Hauptmeier</author>
    <author>Sven Krumke</author>
    <author>Jörg Rambau</author>
    <author>Hans-Christoph Wirth.</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-99-06</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>NP-completeness</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>polynomial-time approximation algorithms</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>stacker-crane problem</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>vehicle routing</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>elevator system</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Eulerian Cycle</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="68Q10">Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.) [See also 68Q85]</collection>
    <collection role="msc" number="68Q25">Analysis of algorithms and problem complexity [See also 68W40]</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="projects" number="ONLINE-PLANNING">ONLINE-PLANNING</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/394/SC-99-06.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/394/SC-99-06.pdf</file>
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