Counting, structure identification and maximum consistency for binary constraint satisfaction problems
Using a framework inspired by Schaefer's generalized satisfiability model [Sch78], Cohen, Cooper and Jeavons [CCJ94] studied the computational complexity of constraint satisfaction problems in the special case when the set of constraints is closed under permutation of labels and domain restriction, and precisely identified the tractable (and intractable) cases.
counting the number of solutions.
structure identification (Dechter and Pearl [DP92]).
approximating the maximum number of satisfiable constraints.
KeywordsPolynomial Time Turing Machine Constraint Satisfaction Problem Constraint Network Satisfying Assignment
Unable to display preview. Download preview PDF.
- [CCJ94]M. Cooper, D. Cohen, and P. Jeavons. Characterizing tractable constraints. Artificial Intelligence, 65:347–361, 1994.Google Scholar
- [CFG+96]D. Clark, J. Frank, I. Gent, E. MacIntyre, N. Tomov, and T. Walsh. Local search and the number of solutions. In E. Render, editor, Principles and Practice of Constraint Programming-CP'96, number 1118 in Lecture Notes in Computer Science, pages 323–337. Springer Verlag, 1996.Google Scholar
- [CH96]N. Creignou and M. Hermann. Complexity of generalized counting problems. Information and Computation, 125(1):1–12, 1996.Google Scholar
- [DI92]R. Dechter and A. Itai. Finding all solutions if you can find one. In Workshop on Tractable Reasoning, AAAI'92, pages 35–39, 1992.Google Scholar
- [DP92]R. Dechter and J. Pearl. Structure identification in relational data. Artificial Intelligence, 58:237–270, 1992.Google Scholar
- [FW]E. Freuder and R. Wallace. Heuristic methods for over-constrained constraint satisfaction problems. In CP'95 Workshop on Over-Constrained Systems.Google Scholar
- [FW92]E. Freuder and R. Wallace. Partial constraint satisfaction. Artificial Intelligence, 58(1-3):21–70, 1992.Google Scholar
- [KMSV94]S. Khanna, R. Motwani, M. Sudan, and U. Vazirani. On syntactic versus computational views of approximability. In Proceedings of the 34th IEEE Symposium on Foundations of Computer Science, pages 819–830. IEEE Computer Society, 1994.Google Scholar
- [Kor95]R. Korf. From approximate to optimal solutions: A case study of number partitioning. In Proceedings of the 14th IJCAI, pages 266–272, 1995.Google Scholar
- [KS96]D. Kavvadias and M. Sideri. The inverse satisfiability problem. In Proceeding of the Second Annual International Computing and Combinatorics Conference, pages 250–259, 1996.Google Scholar
- [KSW96]S. Khanna, M. Sudan, and D. Williamson. A complete classification of the approximability of maximization problems derived from boolean constraint satisfaction. Technical Report TR96-062, Electronic Colloquium on Computational Complexity, http://www.eccc.uni-trier.de/eecc/, 1996.Google Scholar
- [Lau96]H. Lau. A new approach for weighted constraint satisfaction: theoretical and computational results. In E. Freuder, editor, Principles and Practice of Constraint Programming-CP'96, number 1118 in Lecture Notes in Computer Science, pages 323–337. Springer Verlag, 1996.Google Scholar
- [Mac77]A. Mackworth. Consistency in network of relations. Artificial Intelligence, 8:99–118, 1977.Google Scholar
- [MR95]R. Motwani and P. Raghavan. Randomized Algorithms. Cambridge University Press, 1995.Google Scholar
- [Sch78]T. J. Schaefer. The complexity of satisfiability problems. In Proceedings of the 13th ACM Symposium on Theory of Computing, pages 216–226, 1978.Google Scholar
- [SD96]B. Smith and M. Dyer. Locating the phase transition in binary constraint satisfaction problems. Artificial Intelligence Journal, 81(1-2):155–181, 1996.Google Scholar
- [Sel82]A. Selman. Analogues of semirecursive sets and effective reducibilities to the study of NP complexity. Information and Control, 52:36–51, 1982.Google Scholar