Fast scaling algorithms for M-convex function minimization with application to the resource allocation problem

Akiyoshi Shioura

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

M-convex functions, introduced by Murota (Adv. Math. 124 (1996) 272; Math. Prog. 83 (1998) 313), enjoy various desirable properties as "discrete convex functions." In this paper, we propose two new polynomial-time scaling algorithms for the minimization of an M-convex function. Both algorithms apply a scaling technique to a greedy algorithm for M-convex function minimization, and run as fast as the previous minimization algorithms. We also specialize our scaling algorithms for the resource allocation problem which is a special case of M-convex function minimization.

Original languageEnglish
Pages (from-to)303-316
Number of pages14
JournalDiscrete Applied Mathematics
Volume134
Issue number1-3
DOIs
Publication statusPublished - 2004 Jan 5

Keywords

  • Base polyhedron
  • Convex function
  • Discrete optimization
  • Minimization
  • Resource allocation

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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