A combinatorial strongly polynomial algorithm for minimizing submodular functions

Authors:
Satoru Iwata;Lisa Fleischer;Satoru Fujishige
Affiliations:
University of Tokyo, Tokyo, Japan;Carnegie Mellon University, Pittsburgh, Pennsylvania;Osaka University, Toyonaka, Osaka, Japan
Venue:
Journal of the ACM (JACM)
Year:
2001

Citing 15
Cited 85

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Abstract

This paper presents a combinatorial polynomial-time algorithm for minimizing submodular functions, answering an open question posed in 1981 by Grötschel, Lovász, and Schrijver. The algorithm employs a scaling scheme that uses a flow in the complete directed graph on the underlying set with each arc capacity equal to the scaled parameter. The resulting algorithm runs in time bounded by a polynomial in the size of the underlying set and the length of the largest absolute function value. The paper also presents a strongly polynomial version in which the number of steps is bounded by a polynomial in the size of the underlying set, independent of the function values.