A faster strongly polynomial time algorithm for submodular function minimization

Authors:
James B. Orlin
Affiliations:
Sloan School of Management, MIT, 02139, Cambridge, MA, USA
Venue:
Mathematical Programming: Series A and B
Year:
2009

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Abstract

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 5EO + n 6) time, where EO is the time to evaluate f(S) for some $$S \subseteq V$$. This improves the previous best strongly polynomial running time by more than a factor of n. We also extend our result to ring families.