On cardinality constrained polymatroids

Authors:
Jean François Maurras;Ingo Spiegelberg;Rüdiger Stephan
Affiliations:
Laboratoire d'Informatique Fondamentale, UMR 6166, Université de la Mediterranée, Faculté des sciences de Luminy, 163 Avenue de Luminy, 13288 Marseille, France;Zuse Institute Berlin, Takustr. 7, D-14195 Berlin, Germany;Institut für Mathematik, Technische Universität Berlin, Straíe des 17. Juni 136, 10623 Berlin, Germany
Venue:
Discrete Applied Mathematics
Year:
2014

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Abstract

This paper extends results on the cardinality constrained matroid polytope presented in Maurras and Stephan (2011) [8] to polymatroids and the intersection of two polymtroids. Given a polymatroid P"f(S) defined by an integer submodular function f on some set S and an increasing finite sequence c of natural numbers, the cardinality constrained polymatroid is the convex hull of the integer points x@?P"f(S) whose sum of all entries is a member of c. We give a complete linear description for this polytope, characterize some facets of the cardinality constrained version of P"f(S), and briefly investigate the separation problem for this polytope. Moreover, we extend the results to the intersection of two polymatroids.