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International Conference on Integer Programming and Combinatorial Optimization

IPCO 1995: Integer Programming and Combinatorial Optimization pp 50–64Cite as

The interval order polytope of a digraph

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 920))

Abstract

We introduce the interval order polytope of a digraph D as the convex hull of interval order inducing arc subsets of D. Two general schemes for producing valid inequalities are presented. These schemes have been used implicitly for several polytopes and they are applied here to the interval order polytope. It is shown that almost all known classes of valid inequalities of the linear ordering polytope can be explained by the two classes derived from these schemes. We provide two applications of the interval order polytope to combinatorial optimization problems for which to our knowledge no polyhedral descriptions have been given so far. One of them is related to analyzing DNA subsequences.

The first author acknowledges support from the Deutsche Forschungsgemeinschaft under the Sonderforschungsbereich 373. The research of the second author has been supported by the graduate school “Algorithmische Diskrete Mathematik”. The graduate school “Algorithmische Diskrete Mathematik” is supported by the Deutsche Forschungsgemeinschaft, grant We 1265-1.

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Author information

Authors and Affiliations

  1. Institut für Wirtschaftsinformatik, Humboldt-Universität zu Berlin, Spandauer Straße 1, D-10178, Berlin, Germany

    Rudolf Müller

  2. Fachbereich Mathematik (MA 6-1), Technische Universität Berlin, Straße des 17. Juni 136, D-10623, Berlin, Germany

    Andreas S. Schulz

Authors
  1. Rudolf Müller
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  2. Andreas S. Schulz
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Editor information

Egon Balas Jens Clausen

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© 1995 Springer-Verlag Berlin Heidelberg

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Müller, R., Schulz, A.S. (1995). The interval order polytope of a digraph. In: Balas, E., Clausen, J. (eds) Integer Programming and Combinatorial Optimization. IPCO 1995. Lecture Notes in Computer Science, vol 920. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59408-6_41

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  • DOI: https://doi.org/10.1007/3-540-59408-6_41

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-59408-6

  • Online ISBN: 978-3-540-49245-0

  • eBook Packages: Springer Book Archive

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