Date: 01 Jun 2005

The interval order polytope of a digraph

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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.