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 v 1 . . . vn. This vector configuration is then rounded into a {0, 1} solution. We present a procedure called RP R 2 (Random Projection followed by Randomized Rounding) for rounding the solution of such semidefinite programs. We show that the random

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... erplane 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 tradeoff curve (presented by Zwick) that relates the approximation ratio to the size of the maximum cut in a graph.