2015 Volume 7 Pages 69-72
De Klerk-Pasechnik (2002) showed a way to compute the stability number $\alpha(G)$ via copositive programming and proposed LP- and SDP-based approximation schemes for the copositive program. In this paper, we show that their LP-based approximation for the stable set problem is equivalent to a problem of minimizing a quadratic form over a rational grid on the simplex, which can be viewed as a discretized version of the Motzkin-Straus theorem. Furthermore, we provide an algorithm to recover a maximum stable set from an optimal solution of the LP-based approximation and propose a simple local search heuristics for the stable set problem.
