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

Willem Jan van Hoeve
2003 Lecture Notes in Computer Science  
This work presents a hybrid approach to solve the maximum stable set problem, using constraint and semidefinite programming. The approach consists of two steps: subproblem generation and subproblem solution. First we rank the variable domain values, based on the solution of a semidefinite relaxation. Using this ranking, we generate the most promising subproblems first, by exploring a search tree using a limited discrepancy strategy. Then the subproblems are being solved using a constraint
more » ... mming solver. To strengthen the semidefinite relaxation, we propose to infer additional constraints from the discrepancy structure. Computational results show that the semidefinite relaxation is very informative, since solutions of good quality are found in the first subproblems, or optimality is proven immediately. An earlier version of this paper appeared as [18] . 1 Alternative names for the stable set problem are vertex packing, coclique or independent set problem.
doi:10.1007/978-3-540-45193-8_28 fatcat:yhpdj4gc4nflxbxqd5sltf2isi