  Constraint programming uses enumeration and search tree pruning to solve
combinatorial optimization problems. In order to speed up this solution
process, we investigate the use of semidefinite relaxations within constraint
programming. In principle, we use the solution of a semidefinite relaxation to
guide the traversal of the search tree, using a limited discrepancy search
strategy. Furthermore, a semidefinite relaxation produces a bound for the
solution value, which is used to prune parts of the search tree. Experimental
results on stable set and maximum clique problem instances show that constraint
programming can indeed greatly benefit from semidefinite relaxations.
