A push-relabel framework for submodular function minimization and applications to parametric optimization

Authors:
Lisa Fleischer;Satoru Iwata
Affiliations:
Graduate School of Industrial Administration, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, PA;Graduate School of Information Science and Technology, University of Tokyo, Tokyo 113-8656, Japan
Venue:
Discrete Applied Mathematics - Submodularity
Year:
2003

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Abstract

Recently, the first combinatorial strongly polynomial algorithms for submodular function minimization have been devised independently by Iwata, Fleischer, and Fujishige and by Schrijver. In this paper, we improve the running time of Schrijver's algorithm by designing a push-relabel framework for submodular function minimization (SFM). We also extend this algorithm to carry out parametric minimization for a strong map sequence of submodular functions in the same asymptotic running time as a single SFM. Applications include an efficient algorithm for finding a lexicographically optimal base.