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A faster strongly polynomial time algorithm for submodular function minimization

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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.

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  1. Sloan School of Management, MIT, Cambridge, MA, 02139, USA

    James B. Orlin

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  1. James B. Orlin
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Correspondence to James B. Orlin.

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Orlin, J.B. A faster strongly polynomial time algorithm for submodular function minimization. Math. Program. 118, 237–251 (2009). https://doi.org/10.1007/s10107-007-0189-2

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  • DOI: https://doi.org/10.1007/s10107-007-0189-2

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