Abstract
Abstract This chapter surveys how semidefinite programming can be used for finding good approximative solutions to hard combinatorial optimization problems. The chapter begins with a general presentation of several methods for constructing hierarchies of linear and/or semidefinite relaxations for 0/1 problems. Then it moves to an in-depth study of two prominent combinatorial optimization problems: the maximum stable set problem and the max-cut problem. Details are given about the approximation of the stability number by the Lovasz theta number and about the Goemans-Williamson approximation algorithm for max-cut, two results for which semidefinite programming plays an essential role, and we survey some extensions of these approximation results to several other hard combinatorial optimization problems.
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