, Volume 42, Issue 1-3, pp 489-563

Generalized polymatroids and submodular flows

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Abstract

Polyhedra related to matroids and sub- or supermodular functions play a central role in combinatorial optimization. The purpose of this paper is to present a unified treatment of the subject. The structure of generalized polymatroids and submodular flow systems is discussed in detail along with their close interrelation. In addition to providing several applications, we summarize many known results within this general framework.

Supported by a grant from the Alexander von Humboldt Stiftung and by the Institut für Ökonometrie und Operations Research of the University of Bonn, Bonn, Nassestr. 2, Federal Republic of Germany.