Northwest Probability Seminar – Session 1

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. 10:00 AM – 11:00 AM: Coffee and muffins 11:00 AM – 11:40 AM: Random walks with local memory on Z and Z^2 (Lionel Levine, Cornell University) 11:50 AM – 12:30 PM: Stationary diffusions on a space of interval partitions (Noah Forman, University of Oxford/University of Washington) 12:30 PM – 1:40 PM: Lunch

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