An Algorithm for Submodular Functions on Graphs

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

A constructive method is described for proving the Edmonds-Giles theorem which yields a good algorithm provided that a fast subroutine is available for minimizing a submodular set function. The algorithm can be used for finding a maximum weight common independent set of two matroids, for finding a minimum weight covering of directed cuts of a digraph, and, as a new application, for finding a minimum cost k strongly connected orientation of an undirected graph. As a theoretical consequence of the algorithm, we prove a combinatorial feasibility theorem for Edmonds-Giles polyhedron and then we derive a discrete separation theorem which says, roughly, an integer valued submodular function B and an integer valued supermodular function R can be separated by an integer valued modular function provided that R ≤B.

Original languageEnglish
Pages (from-to)97-120
Number of pages24
JournalNorth-Holland Mathematics Studies
Volume66
Issue numberC
DOIs
Publication statusPublished - 1982

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Submodular Function
Integer
Graph in graph theory
Separation Theorem
Modular Functions
Independent Set
Matroid
Theorem
Undirected Graph
Digraph
Polyhedron
Covering
Costs

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

An Algorithm for Submodular Functions on Graphs. / Frank, A.

In: North-Holland Mathematics Studies, Vol. 66, No. C, 1982, p. 97-120.

Research output: Contribution to journalArticle

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