A faster strongly polynomial time algorithm for submodular function minimization

We consider the problem of minimizing a submodular function f defined on a set V with n elements. We give a combinatorial algorithm that runs in O( n 5 EO  +  n 6 ) time, where EO is the time to evaluate f ( S ) for some . This improves the previous best strongly polynomial running time by more than...

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Bibliographic Details
Published in:Mathematical programming Vol. 118; no. 2; pp. 237 - 251
Main Author: Orlin, James B.
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer-Verlag 01.05.2009
Springer
Springer Nature B.V
Subjects:
Algorithms
Applied sciences
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Deadlines
Exact sciences and technology
Flows in networks. Combinatorial problems
Full Length Paper
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Operational research and scientific management
Operational research. Management science
Theoretical
Corner Point
Distance Vector
Distance Function
Combinatorial Algorithm
Greedy Algorithm
Submodular function
Function minimization
Ring
Polynomial method
Combinatorial optimization
Mathematical programming
Polynomial time
ISSN:0025-5610, 1436-4646
Online Access:Get full text
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Summary:We consider the problem of minimizing a submodular function f defined on a set V with n elements. We give a combinatorial algorithm that runs in O( n 5 EO  +  n 6 ) time, where EO is the time to evaluate f ( S ) for some . This improves the previous best strongly polynomial running time by more than a factor of n . We also extend our result to ring families.
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-007-0189-2