Local max-cut in smoothed polynomial time release_4sxw7tkplrd5jh2hsq4tlbqkua

by Omer Angel and Sébastien Bubeck and Yuval Peres and Fan Wei

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In 1988, Johnson, Papadimitriou and Yannakakis wrote that "Practically all the empirical evidence would lead us to conclude that finding locally optimal solutions is much easier than solving NP-hard problems". Since then the empirical evidence has continued to amass, but formal proofs of this phenomenon have remained elusive. A canonical (and indeed complete) example is the local max-cut problem, for which no polynomial time method is known. In a breakthrough paper, Etscheid and Röglin proved that the smoothed complexity of local max-cut is quasi-polynomial, i.e., if arbitrary bounded weights are randomly perturbed, a local maximum can be found in n^O( n) steps. In this paper we prove smoothed polynomial complexity for local max-cut, thus confirming that finding local optima for max-cut is much easier than solving it.
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Type  article
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Date   2016-12-01
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arXiv  1610.04807v2
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