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Title: Combinatorial Approximation Algorithms for MaxCut using Random Walks

Speaker: C. Seshadhri (Sandia National Labs, Livermore)

Abstract: We give the first combinatorial approximation algorithm for Maxcut that beats the trivial 0.5 factor by a constant. The main partitioning procedure is very intuitive, natural, and easily described. It essentially performs a number of random walks and aggregates the information to provide the partition. We can control the running time to get an approximation factor-running time tradeoff. We show that for any constant b > 1.5, there is an O(n^b)-time combinatorial algorithm that outputs a (0.5+delta)-approximation for Maxcut, where delta = delta(b) is some positive constant. The analysis of this algorithm goes via Trevisan's eigenvalue analysis for MaxCut. One of the components of our algorithm is a weak local graph partitioning procedure that may be of independent interest.

Joint work with Satyen Kale. To appear in ICS 2011.