PRIMAL-DUAL ALGORITHM FOR SUBMODULAR FLOWS.

William H. Cunningham, Andras Frank

Research output: Contribution to journalArticle

34 Citations (Scopus)

Abstract

Previously the only polynomial-time solution algorithm to solve the optimal submodular flow problem introduced by J. Edmonds and R. Giles was based on the ellipsoid method. Here, modulo an efficient oracle for minimizing certain submodular functions, a polynomial time procedure is presented which uses only combinatorial steps (like building auxiliary digraphs, finding augmenting paths). The minimizing oracle is currently available only via the ellipsoid method, in general; however in important special cases, such as network flows, matroid intersections, orientations, and directed cut coverings, the necessary oracle can be provided combinatorially.

Original languageEnglish
Pages (from-to)251-262
Number of pages12
JournalMathematics of Operations Research
Volume10
Issue number2
DOIs
Publication statusPublished - Jan 1 1985

ASJC Scopus subject areas

  • Mathematics(all)
  • Computer Science Applications
  • Management Science and Operations Research

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