Published on November 14, 2016 by Microsoft Research

The local max-cut problem asks to find a partition of the vertices in a weighted graph such that the cut weight cannot be improved by moving a single vertex (that is the partition is locally optimal). This comes up naturally, for example, in computing Nash equilibrium for the party affiliation game. It is well-known that the natural local search algorithm for this problem might take exponential time to reach a locally optimal solution. We show that adding a little bit of noise to the weights tames this exponential into a polynomial. In particular we show that local max-cut is in smoothed polynomial time (this improves the recent quasi-polynomial result of Etscheid and Roglin). Joint work with Omer Angel, Yuval Peres, and Fan Wei.

See more on this video at www.microsoft.com/en-us/research/video/northwest-probability-seminar-session-3/

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Tom Hutchcroft
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Tom Hutchcroft
15 days 16 hours ago

Slides from the talk are available on my website www.math.ubc.ca/~thutch/

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