Complexity of conservative constraint satisfaction problems

ACM Transactions on Computational Logic

Volumn 12, Issue 4, 2011, Pages

  Bulatov, Andrei A ^a  

^a SIMON FRASER UNIVERSITY   (Canada)

Author keywords

Complexity; Constraint satisfaction problem; Dichotomy theorem; Homomorphism problem

Indexed keywords

ALGEBRAIC APPROACHES; COMPLEXITY; CONSTRAINT LANGUAGE; CONSTRAINT SATISFACTION PROBLEM; CONSTRAINT SATISFACTION PROBLEMS; DICHOTOMY THEOREM; HOMOMORPHISM PROBLEM; NP COMPLETE; POLYNOMIAL-TIME; RESEARCH DIRECTIONS; SOLVING ALGORITHM;

POLYNOMIAL APPROXIMATION;

EID: 80051943600     PISSN: 15293785     EISSN: 1557945X     Source Type: Journal    
DOI: 10.1145/1970398.1970400     Document Type: Article

References (45)

1. BAKER, K. AND PIXLEY, A. 1975. Polynomial interpolation and the chinese remainder theorem. Math. Zeit. 143, 165-174.
2. BREWSTER, R. C., FEDER, T., HELL, P., HUANG, J., AND MACGILLIVRAY, G. 2008. Near-unanimity functions and varieties of reflexive graphs. SIAM J. Discrete Math. 22, 3, 938-960.
3. BULATOV, A. 2002a. A dichotomy theorem for constraints on a three-element set. In Proceedings of the 43rd IEEE Symposium on Foundations of Computer Science (FOCS'02). 649-658.
4. BULATOV, A. 2002b. Mal'tsev constraints are tractable. Tech. rep. PRG-RR-02-05. Computing Laboratory, University of Oxford, Oxford, U.K.
5. BULATOV, A. 2006a. Combinatorial problems raised from 2-semilattices. J. Alg. 298, 2, 321-339. (Pubitemid 43574674)
6. BULATOV, A. AND JEAVONS, P. 2000. Tractable constraints closed under a binary operation. Tech. rep. PRG-TR- 12-00. Computing Laboratory, University of Oxford, Oxford, U.K.
7. BULATOV, A. AND JEAVONS, P. 2001a. Algebraic approach to multi-sorted constraints. Tech. rep. PRG-RR-01-18. Computing Laboratory, University of Oxford, Oxford, U.K.
8. BULATOV, A. AND JEAVONS, P. 2001b. Algebraic structures in combinatorial problems. Tech. rep. MATH-AL-4-2001. Technische Universität Dresden, Dresden, Germany. http://web.comlab.ox.ac.uk/oucl/research/areas/constraints/ publications/index.html.
9. BULATOV, A. AND JEAVONS, P. 2003. An algebraic approach to multi-sorted constraits. In Proceedings of the 9th International Conference on Principles and Practice of Constraint Programming. 197-202.
10. BULATOV, A., JEAVONS, P., AND KROKHIN, A. 2001. The complexity of maximal constraint languages. In Proceedings of the 33rd Annual ACM Simposium on Theory of Computing. 667-674. (Pubitemid 32865784)
11. BULATOV, A., JEAVONS, P., AND KROKHIN, A. 2003. Functions of multiple-valued logic and the complexity of constraint satisfaction: A short survey. In Proceedings of 33rd IEEE International Symposium on Multiple-Valued Logic. 343-351.
12. BULATOV, A. A. 2006b. A dichotomy theorem for constraint satisfaction problems on a 3-element set. J. ACM 53, 1, 66-120.
13. BULATOV, A. A. AND DALMAU, V. 2006. A simple algorithm for Mal'tsev constraints. SIAM J. Comput. 36, 1, 16-27. (Pubitemid 46374016)
14. BULATOV, A. A., JEAVONS, P., AND KROKHIN, A. A. 2005. Classifying the complexity of constraints using finite algebras. SIAM J. Comput. 34, 3, 720-742. (Pubitemid 40844240)
15. COHEN, D., COOPER, M., AND JEAVONS, P. 1994. Characterising tractable constraints. Art. Intell. 65, 2, 347-361.
16. CREIGNOU, N., KHANNA, S., AND SUDAN, M. 2001. Complexity Classifications of Boolean Constraint Satisfaction Problems. SIAM Monographs on Discrete Mathematics and Applications, vol. 7. SIAM, Philadelphia, PA.
17. DALMAU, V. 2000. A new tractable class of constraint satisfaction problems. In Proceedings of the 6th International Symposium on Artificial Intelligence and Mathematics.
18. DALMAU, V. 2002. Constraint satisfaction problems in non-deterministic logarithmic space. In Proceedings of the 29th International Colloquium on Automata, Languages and Programming. Lecture Notes in Computer Science, vol. 2380. Springer-Verlag, Berlin, Germany, 414-425.
19. DECHTER, R. 2003. Constraint processing. Morgan Kaufmann, San Francisco, CA.
20. DENECKE, K. AND WISMATH, S. 2002. Universal Algebra and Applications in Theoretical Computer Science. Chapman and Hall/CRC Press, Boca Raton, FL.
21. DYER, M. AND GREENHILL, C. 2000. The complexity of counting graph homomorphisms. Random Struct. Algor. 17, 260-289.
22. FEDER, T. AND HELL, P. 1998. List homomorphisms to reflexive graphs. J. Combin. Theor. B 72, 236-250. (Pubitemid 128347498)
23. FEDER, T. AND HELL, P. 2003. Restricted list constraints and list partitions. Unpublished manuscript.
24. FEDER, T., HELL, P., AND HUANG, J. 1999. List homomorphisms and circular arc graphs. Combinatorica 19, 487-505.
25. FEDER, T., HELL, P., AND HUANG, J. 2003. Bi-arc graphs, and the complexity of list homomorphisms. J. Graph Theor. 42, 1, 61-80.
26. FEDER, T. AND VARDI, M. 1998. The computational structure of monotone monadic SNP and constraint satisfaction: A study through datalog and group theory. SIAM J. Comput. 28, 57-104. (Pubitemid 128491791)
27. GALUCCIO, A., HELL, P., AND NE?SETR?RIL, J. 2000. The complexity of H-Coloring of bounded degree graphs. Discrete Math., 101-109.
28. GOTTLOB, G., LEONE, N., AND SCARCELLO, F. 1999. Hypertree decompositions and tractable queries. In Proceedings of the 18th Symposium on Principles of Database Systems. 21-32.
29. HELL, P. AND NE?SET?RIL, J. 1990. On the complexity of H-Coloring. J. Combin. Theor. Ser. B 48, 92-110.
30. JEAVONS, P. 1998. On the algebraic structure of combinatorial problems. Theoret. Comp. Sci. 200, 185-204. (Pubitemid 128450816)
31. JEAVONS, P., COHEN, D., AND COOPER, M. 1998a. Constraints, consistency and closure. Art. Intell. 101, 1-2, 251-265. (Pubitemid 128387395)
32. JEAVONS, P., COHEN, D., AND GYSSENS, M. 1997. Closure properties of constraints. J. ACM 44, 527-548. (Pubitemid 127617702)
33. JEAVONS, P., COHEN, D., AND PEARSON, J. 1998b. Constraints and universal algebra. Ann. Math. Art. Intell. 24, 51-67. (Pubitemid 128404015)
34. KEARNES, K. 1996. Idempotent simple algebras. In Logic and Algebra, Lecture Notes in Pure and Applied Mathematics, vol. 180, Dekker, New York, NY, 529-572.
35. KOLAITIS, P. 2003. Constraint satisfaction, databases, and logic. In Proceedings of the 17th International Joint Conference on Artificial Intellignece.
36. KOLAITIS, P. AND VARDI, M. 2000a. Conjunctive-query containment and constraint satisfaction. J. Comput. Syst. Sci. 61, 302-332.
37. KOLAITIS, P. AND VARDI, M. 2000b. A game-theoretic approach to constraint satisfaction. In Proceedings of the 17th National (U.S.) Conference on Artificial Intelligence. 175-181.
38. KRATOCHVIL, J. AND TUZA, Z. 1994. Algorithmic complexity of list colorings. Discrete Appl. Math. 50, 297-302.
39. LAROSE, B. AND ZADORI, L. 2007. Bounded width problems and algebras. Alg. Universalis 56, 3-4, 439-466.
40. MONTANARI, U. 1974. Networks of constraints: Fundamental properties and applications to picture processing. Inform. Sci. 7, 95-132.
41. PIPPENGER, N. 1997. Theories of Computability. Cambridge University Press, Cambridge, U.K.
42. P?SCHEL, R. AND KALUŽNIN, L. 1979. Funktionen- und Relationenalgebren. DVW, Berlin, Germany.
43. POST, E. 1941. The Two-Valued Iterative Systems of Mathematical Logic. Annals of Mathematical Studies, vol. 5. Princeton University Press, Princeton, NJ.
44. SCHAEFER, T. 1978. The complexity of satisfiability problems. In Proceedings of the 10th ACM Symposium on Theory of Computing. 216-226.
45. SZENDREI, A. 1986. Clones in Universal Algebra. Seminaires de Mathematiques Superieures, vol. 99. Universit É de Móntreal, Montreal, Quebec, Canada.