The RPR2 rounding technique for semidefinite programs

Authors:
Uriel Feige;Michael Langberg
Affiliations:
Department of Computer Science and Applied Mathematics, Weizmann Institute of Sciene, Rehovot, Israel;Department of Computer Science, California Institute of Technology, Pasadena, CA and Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel
Venue:
Journal of Algorithms
Year:
2006

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Abstract

Several combinatorial optimization problems can be approximated using algorithms based on semidefinite programming. In many of these algorithms a semidefinite relaxation of the underlying problem is solved yielding an optimal vector configuration v1,...,vn. This vector configuration is then rounded into a {0, 1} solution. We present a procedure called RPR2 (Random Projection followed by Randomized Rounding) for rounding the solution of such semidefinite programs. We show that the random hyperplane rounding technique introduced by Goemans and Williamson, and its variant that involves outward rotation, are both special cases of RPR2. We illustrate the use of RPR2 by presenting two applications. For Max-Bisection we improve the approximation ratio. For Max-Cut, we improve the tradeoff curve (presented by Zwick) that relates the approximation ratio to the size of the maximum cut in a graph.