NDLI: Local max-cut in smoothed polynomial time

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Local max-cut in smoothed polynomial time

Content Provider	ACM Digital Library
Author	Bubeck, Sébastien Peres, Yuval Wei, Fan Angel, Omer
Abstract	In 1988, Johnson, Papadimitriou and Yannakakis wrote that â 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 RÃ¶glin 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 Ï $n^{O(logn)}$ steps where Ï is an upper bound on the random edge weight density. 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. .
Starting Page	429
Ending Page	437
Page Count	9
File Format	PDF
ISBN	9781450345286
DOI	10.1145/3055399.3055402
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2017-06-19
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Smoothed analysis Hopfield network Polynomial running time Nash equilibrium Sherrington-kirkpatrick model Potential game Max-cut
Content Type	Text
Resource Type	Article

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