Submodular function minimization and related topics

It had been a long-standing open problem to devise a combinatorial polynomial algorithm for minimizing submodular functions. Iwata-Fleischer-Fujishige (IFF) and Schrijver resolved the problem independently and simultaneously. The present article is basically a survey, though not comprehensive, on su...

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Bibliographic Details
Published inOptimization methods & software Vol. 18; no. 2; pp. 167 - 180
Main Author Fujishige, Satoru
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 01.04.2003
Subjects
Combinatorial Algorithm
Polynomial Algorithm
Submodular Function
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ISSN1055-6788
1029-4937
DOI10.1080/1055678031000081447

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Summary:It had been a long-standing open problem to devise a combinatorial polynomial algorithm for minimizing submodular functions. Iwata-Fleischer-Fujishige (IFF) and Schrijver resolved the problem independently and simultaneously. The present article is basically a survey, though not comprehensive, on submodular function minimization algorithms and also describes additional results and research subjects. In this article we first give an outline of the IFF algorithm and then show two modifications of the original IFF algorithm, which seem to be promising in practical implementation. We also describe a brief history of developments in submodular function minimization. Finally, we furnish some possible future research subjects in submodular function minimization.
ISSN:1055-6788
1029-4937
DOI:10.1080/1055678031000081447