The RPR 2 rounding technique for semide nite programsUriel

Several combinatorial optimization problems can be approximated using algorithms based on semideenite programming. In many of these algorithms a semideenite relaxation of the underlying problem is solved yielding an optimal vector connguration v 1 : : : v n. This vector connguration is then rounded into a f0; 1g solution. We present a procedure called RP R 2 (Random Projection followed by Randomized Rounding) for rounding the solution of such semideenite 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 RP R 2. We illustrate the use of RP R 2 by presenting two applications. For Max-Bisection we improve the approximation ratio. For Max-Cut, we improve the tradeoo curve (presented by Zwick) that relates the approximation ratio to the size of the maximum cut in a graph.