Combinatorial Approximation Algorithms for MAXCUT using Random Walks.
Year: 2011
Type: article
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 Õ(nb) algorithm that outputs a (0.5 + δ)-approximation for MAXCUT, where δ = δ(b) is some positive constant. One of the components of our algorithm is a weak local graph partitioning procedure that may be of independent interest. Given a starting vertex i and a conductance parameter φ, unless a random walk of length ℓ = O(log n) starting from i mixes rapidly (in terms of φ and ℓ), we can find a cut of conductance at most φ close to the vertex. The work done per vertex found in the cut is sublinear in n.
Authors: Satyen Kale, C. Seshadhri
Institutions: Yahoo (United Kingdom), Sandia National Laboratories
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2963382491