Substitutes and complements in network flows viewed as discrete convexity

Kazuo Murota, Akiyoshi Shioura

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


We study combinatorial properties of the optimal value function of the network flow problem. It is shown by Gale-Politof [Substitutes and complements in networks flow problems, Discrete Appl. Math. 3 (1981) 175-186] that the optimal value function has submodularity and supermodularity w.r.t. problem parameters such as weights and capacities. In this paper we shed a new light on this result from the viewpoint of discrete convex analysis to point out that the submodularity and supermodularity are naturally implied by discrete convexity, called M-convexity and L-convexity, of the optimal value function.

Original languageEnglish
Pages (from-to)256-268
Number of pages13
JournalDiscrete Optimization
Issue number3
Publication statusPublished - 2005 Sept
Externally publishedYes


  • Combinatorial optimization
  • Discrete convexity
  • Network flow
  • Submodularity

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Applied Mathematics


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