Semideenite Relaxations, Multivariate Normal Distributions, and Order Statistics

We propose two new dependent randomized rounding algorithms for approximating the global maximum of a quadratic program subject to linear as well as boolean constraints. We show that the rst of these methods based on the multivariate normal distribution, provides (a) a 0.878 approximation algorithm for s ?t max-cut problems, (b) a 0.878 approximation algorithm for the max-cut problem that has the property that the expected number of nodes in one part of the cut is n=2, (c) a 0.878 approximation algorithm for s ? u ? v max-cut problems with probability at least 0.91, and (d) a guarantee on the degree of infeasibility and suboptimality for quadratic optimization with linear constraints. The second of those methods based on order statistics provides near optimal solutions on maximum bisection problems on graphs with up to 1,000 nodes.