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This work presents a hybrid approach to solve the maximum stable set prob- lem, using constraint and semidenite programming. The approach consists of two steps: subproblem generation and subproblem solution. First we rank the vari- able domain values, based on the solution of a semidenite relaxation. Using this ranking, we generate the most promising subproblems rst, by exploring a search tree using a limited discrepancy strategy. Then the subproblems are being solved using a constraint programming solver. To strengthen the semidenite relaxation, we propose to infer additional constraints from the discrepancy structure. Com- putational results show that the semidenite relaxation is very informative, since solutions of good quality are found in the rst subproblems, or optimality is proven immediately.

A Hybrid Constraint Programming and Semidefinite Programming Approach for the Stable Set Problem