<?xml version="1.0" encoding="utf-8"?>
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  <doc>
    <id>7471</id>
    <completedYear/>
    <publishedYear>2020</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>100552</pageFirst>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue>35</issue>
    <volume/>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2019-08-20</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Separation of cycle inequalities in periodic timetabling</title>
    <abstract language="eng">Cycle inequalities play an important role in the polyhedral study of the periodic timetabling problem in public transport. We give the first pseudo-polynomial time separation algorithm for cycle inequalities, and we contribute a rigorous proof for the pseudo-polynomial time separability of the change-cycle inequalities. Moreover, we provide several NP-completeness results, indicating that pseudo-polynomial time is best possible. The efficiency of these cutting planes is demonstrated on real-world instances of the periodic timetabling problem.</abstract>
    <parentTitle language="eng">Discrete Optimization</parentTitle>
    <identifier type="doi">10.1016/j.disopt.2019.100552</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-69746</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Niels Lindner</submitter>
    <author>Heide Hoppmann</author>
    <author>Marika Karbstein</author>
    <author>Niels Lindner</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="hoppmann">Hoppmann, Heide</collection>
    <collection role="projects" number="ECMath-MI3">ECMath-MI3</collection>
    <collection role="persons" number="lindner">Lindner, Niels</collection>
    <collection role="projects" number="ECMath-MI7">ECMath-MI7</collection>
    <collection role="projects" number="MODAL-MobilityLab">MODAL-MobilityLab</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
</export-example>
