Improved algorithms for 3-coloring, 3-edge-coloring, and constraint satisfaction
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
CP '02 Proceedings of the 6th International Conference on Principles and Practice of Constraint Programming
Exact algorithms for NP-hard problems: a survey
Combinatorial optimization - Eureka, you shrink!
CSCLP'04 Proceedings of the 2004 joint ERCIM/CoLOGNET international conference on Recent Advances in Constraints
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CSP search algorithms are exponential in the worst-case. A trivial upper bound on the time complexity of CSP search algorithms is O*(dn), where n and d are the number of variables and the maximal domain size of the underlying CSP, respectively. In this paper we show that a combination of heuristic methods of constraint solving can reduce the time complexity. In particular, we prove that the FC-CBJ algorithm combined with the fail-first variable ordering heuristic (FF) achieves time complexity of O*((d – 1)n), where n and d are the number of variables and the maximal domain size of the given CSP, respectively. Furthermore, we show that the combination is essential because neither FC-CBJ alone nor FC with FF achieve the above complexity. The proposed results are interesting because they establish connection between theoretical and practical approaches to CSP research.