A constructive proof for the induction of M-convex functions through networks

A. Shioura

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

Murota (1995) introduced an M-convex function as a quantitative generalization of the set of integral vectors in an integral base polyhedron as well as an extension of valuated matroid over base polyhedron. Just as a base polyhedron can be transformed through a network, an M-convex function can be induced through a network. This paper gives a constructive proof for the induction of an M-convex function. The proof is based on the correctness of a simple algorithm, which finds an exchangeable element. We also analyze a behavior of induced functions when they take the value -∞.

Original languageEnglish
Pages (from-to)271-278
Number of pages8
JournalDiscrete Applied Mathematics
Volume82
Issue number1-3
DOIs
Publication statusPublished - 1998 Mar 2

Keywords

  • Base polyhedron
  • Convex function
  • Matroid
  • Submodular system

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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