Northwest Probability Seminar – Session 2

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. 2:20 PM – 3:10 PM: Branching graphs and Integrable Probability (Alexei Borodin, MIT; Birnbaum lecture) 3:20 PM – 4:00 PM: Local max-cut in smoothed polynomial time (Sébastien Bubeck, Microsoft Research) 4:00 PM – 4:30 PM: Tea and snacks

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