Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Connections between semidefinite relaxations of the max-cut and stable set problems
Mathematical Programming: Series A and B
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
Computational Experience with Stable Set Relaxations
SIAM Journal on Optimization
Reduced Cost-Based Ranking for Generating Promising Subproblems
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Simple and Fast: Improving a Branch-And-Bound Algorithm for Maximum Clique
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
A fast algorithm for the maximum clique problem
Discrete Applied Mathematics - Sixth Twente Workshop on Graphs and Combinatorial Optimization
Solving Graph Bisection Problems with Semidefinite Programming
INFORMS Journal on Computing
Principles of Constraint Programming
Principles of Constraint Programming
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
k-Clustering Minimum Biclique Completion via a Hybrid CP and SDP Approach
CPAIOR '09 Proceedings of the 6th International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
A simple and faster branch-and-bound algorithm for finding a maximum clique
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
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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.