The interval order polytope of a digraph

  • Rudolf Müller
  • Andreas S. Schulz
Conference paper

DOI: 10.1007/3-540-59408-6_41

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

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.

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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Rudolf Müller
    • 1
  • Andreas S. Schulz
    • 2
  1. 1.Institut für WirtschaftsinformatikHumboldt-Universität zu BerlinBerlinGermany
  2. 2.Fachbereich Mathematik (MA 6-1)Technische Universität BerlinBerlinGermany

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