Strongly polynomial and fully combinatorial algorithms for bisubmodular function minimization

Bisubmodular functions are a natural “directed”, or “signed”, extension of submodular functions with several applications. Recently Fujishige and Iwata showed how to extend the Iwata, Fleischer, and Fujishige (IFF) algorithm for submodular function minimization (SFM) to bisubmodular function minimiz...

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Vydáno v:Mathematical programming Ročník 122; číslo 1; s. 87 - 120
Hlavní autoři: McCormick, S. Thomas, Fujishige, Satoru
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer-Verlag 01.03.2010
Springer
Springer Nature B.V
Témata:
Algorithms
Applied sciences
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Exact sciences and technology
Flows in networks. Combinatorial problems
Full Length Paper
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical programming
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Operational research and scientific management
Operational research. Management science
Optimization
Optimization algorithms
Polynomials
Studies
Theoretical
Secondary: 90C27
68W40
Primary: 65K05
Submodular function
Function minimization
Polynomial method
Combinatorial optimization
Mathematical programming
ISSN:0025-5610, 1436-4646
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Popis
Shrnutí:Bisubmodular functions are a natural “directed”, or “signed”, extension of submodular functions with several applications. Recently Fujishige and Iwata showed how to extend the Iwata, Fleischer, and Fujishige (IFF) algorithm for submodular function minimization (SFM) to bisubmodular function minimization (BSFM). However, they were able to extend only the weakly polynomial version of IFF to BSFM. Here we investigate the difficulty that prevented them from also extending the strongly polynomial version of IFF to BSFM, and we show a way around the difficulty. This new method gives a somewhat simpler strongly polynomial SFM algorithm, as well as the first combinatorial strongly polynomial algorithm for BSFM. This further leads to extending Iwata’s fully combinatorial version of IFF to BSFM.
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-008-0242-9