Recognizing frozen variables in constraint satisfaction problems

Theoretical Computer Science

Volumn 329, Issue 1-3, 2004, Pages 93-113

  Jonsson, Peter ^a   Krokhin, Andrei ^b  

^a LINKÖPING UNIVERSITY   (Sweden)

^b DURHAM UNIVERSITY   (United Kingdom)

Author keywords

Computational complexity; Constraint satisfaction; Frozen variable; Polymorphism

Indexed keywords

BOOLEAN FUNCTIONS; COMPUTATIONAL COMPLEXITY; COMPUTER SCIENCE; CONSTRAINT THEORY; DATABASE SYSTEMS; MATHEMATICAL OPERATORS; SECURITY OF DATA; SET THEORY; STATISTICAL METHODS;

CONSTRAINT SATISFACTION PROBLEM (CSP); DOMAIN SIZES; FROZEN VARIABLES; POLYMORPHISM;

PROBLEM SOLVING;

EID: 10044257924     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2004.08.006     Document Type: Article

References (46)

1. N. Adam, J. Wortman, Security-control methods for statistical databases: a comparative study, ACM Comput. Surv. 21 (4) (1989) 515-556.
2. B. Bollobás, C. Borgs, J. Chayes, J. Kim, D. Wilson, The scaling window of the 2-SAT transition, Random Struct. Algorithms 18 (3) (2001) 201-256.
3. F. Börner, A. Bulatov, P. Jeavons, A. Krokhin, Quantified constraints: algorithms and complexity, in: Proceedings 17th Workshop on Computer Science Logic CSL'03, 2003, pp. 58-70.
4. A. Bulatov, Mal'tsev constraints are tractable, Technical Report PRG-RR-02-05, Computing Laboratory, University of Oxford, UK, 2002.
5. A. Bulatov, A dichotomy theorem for constraints on a three-element set, in: Proceedings of 43rd IEEE Symposium on Foundations of Computer Science, FOCS'02, 2002, pp. 649-658.
6. A. Bulatov, Tractable conservative constraint satisfaction problems, in: Proceedings 18th IEEE Symposium on Logic in Computer Science, LICS'03, 2003, pp. 321-330.
7. A. Bulatov, P. Jeavons, Tractable constraints closed under a binary operation, Technical Report PRG-TR-12-00, Computing Laboratory, University of Oxford, UK, 2000.
8. A. Bulatov, P. Jeavons, A. Krokhin, Classifying complexity of constraints using finite algebras, SIAM J. Comput., accepted for publication.
9. A. Bulatov, A. Krokhin, P. Jeavons, Constraint satisfaction problems and finite algebras, in: Proceedings 27th International Colloquium on Automata, Languages and Programming, ICALP'00, Vol. 1853, Lecture Notes in Computer Science, Springer, Berlin, 2000, pp. 272-282.
10. A. Bulatov, A. Krokhin, P. Jeavons, The complexity of maximal constraint languages, in: Proceedings 33rd ACM Symposium on Theory of Computing STOC'01, 2001, pp. 667-674.
11. N. Creignou, S. Khanna, M. Sudan, Complexity Classifications of Boolean Constraint Satisfaction Problems, Vol. 7, SIAM Monographs on Discrete Mathematics and Applications, 2001.
12. J. Culberson, I. Gent, Frozen development in graph coloring, Theoret. Comput. Sci. 265 (1-2) (2001) 227-264.
13. V. Dalmau, Constraint satisfaction problems in non-deterministic logarithmic space, in: Proceedings of the 29th International Colloquium on Automata, Languages and Programming, ICALP'02, Vol. 2380, Lecture Notes in Computer Science, Springer, Berlin, 2002, pp. 414-425.
14. T. Feder, P. Hell, J. Huang, List homomorphisms and circular arc graphs, Combinatorica 19 (1999) 487-505.
15. T. Feder, P. Hell, J. Huang, Bi-arc graphs and the complexity of list homomorphisms, J. Graph Theory 42 (2003) 61-80.
16. T. Feder, M. Vardi, The computational structure of monotone monadic SNP and constraint satisfaction: a study through Datalog and group theory, SIAM J. Comput. 28 (1998) 57-104.
17. C. Gomes, B. Selman, H. Kautz, Heavy-tailed phenomena in satisfiability and constraint satisfaction, J. Automat. Reasoning 24 (2000) 67-100.
18. G. Gottlob, L. Leone, F. Scarcello, Hypertree decomposition and tractable queries, J. Comput. System Sci. 64 (3) (2002) 579-627.
19. M. Grohe, The complexity of homomorphism and constraint satisfaction problems seen from the other side, in: Proceedings of the 44th Symposium on Foundations of Computer Science, FOCS'2003, 2003, pp. 552-561.
20. J. Hastad, Some optimal inapproximability results, J. ACM 48 (2001) 798-859.
21. P. Hell, J. Nešetřil, On the complexity of H-coloring, J. Combin. Theory, Ser. B 48 (1990) 92-110.
22. P. Jeavons, On the algebraic structure of combinatorial problems, Theoret. Comput. Sci. 200 (1998) 185-204.
23. P. Jeavons, D. Cohen, M. Gyssens, Closure properties of constraints, J. ACM 44 (1997) 527-548.
24. P. Jeavons, D. Cohen, M. Gyssens, How to determine the expressive power of constraints, Constraints 4 (1999) 113-131.
25. L. Juban, Dichotomy theorem for generalized unique satisfiability problem, in: Proceedings of the 12th Conference on Fundamentals of Computation Theory, FCT'99, Vol. 1684, Lecture Notes in Computer Science, Springer, Berlin, 1999, pp. 327-337.
26. H. Kautz, B. Selman, Planning as satisfiability, in: Proceedings of the 10th European Conference on Artificial Intelligence, ECAI'92, 1992, pp. 359-363.
27. J. Kleinberg, C.H. Papadimitriou, P. Raghavan, Auditing Boolean attributes, J. Comput. System Sci. 66 (2003) 244-253.
28. P. Kolaitis, M. Vardi, Conjunctive-query containment and constraint satisfaction, J. Comput. System Sci. 61 (2000) 302-332.
29. A. Krokhin, A. Bulatov, P. Jeavons, Functions of multiple-valued logic and the complexity of constraint satisfaction: a short survey, in: Proceedings of the 33rd IEEE International Symposium on Multiple-Valued Logic, ISMVL'03, 2003, pp. 343-351.
30. K. Marriott, P. Stuckey, Programming with Constraints: an Introduction, MIT Press, Cambridge, MA, 1998.
31. R. Monasson, R. Zecchina, S. Kirkpatrick, B. Selman, L. Troyansky, 2+p-SAT: relation of typical-case complexity to the nature of phase transition, Random Struct. Algorithms 15 (3-4) (1999) 414-440.
32. U. Montanari, Networks of constraints: fundamental properties and applications to picture processing, Inform. Sci. 7 (1974) 95-132.
33. C. Papadimitriou, Computational Complexity, Addison-Wesley, Reading, MA, 1994.
34. C. Papadimitriou, D. Wolfe, The complexity of facets resolved, J. Comput. System Sci. 37 (1) (1988) 2-13.
35. C. Papadimitriou, M. Yannakakis, The complexity of facets and some facets of complexity, J. Comput. System Sci. 28 (2) (1982) 244-259.
36. A. Parkes, Clustering at the phase transition, in: Proceedings of the 14thNational (US) Conference on Artificial Intelligence, AAAI'97, 1997, pp. 340-345.
37. N. Pippenger, Theories of Computability, Cambridge University Press, Cambridge, 1997.
38. R. Pöschel, Galois connections for operations and relations, Technical Report, MATH-AL-8-2001, Technische Universität Dresden, Germany, 2001.
39. R. Pöschel, L. Kalužnin, Funktionen- und Relationenalgebren, DVW, Berlin, 1979.
40. E. Post, The two-valued iterative systems of mathematical logic, Annals Mathematical Studies, Vol. 5, Princeton University Press, Princeton, NJ, 1941.
41. I. Rosenberg, Minimal clones I: the five types, in: Lectures in Universal Algebra (Proc. Conf. Szeged, 1983), Vol. 43 Colloqium of Mathematical Society Janos Bolyai, North-Holland, Amsterdam, 1986, pp. 405-427.
42. T. Schaefer, The complexity of satisfiability problems, in: Proceedings 10th ACM Symposium on Theory of Computing STOC'78, 1978, pp. 216-226.
43. J. Singer, I. Gent, A. Smaill, Backbone fragility and the local search cost peak, J. Artif. Intell. Res. 12 (2000) 235-270.
44. A. Szendrei, Clones in Universal Algebra, Vol. 99, Seminaires de Mathematiques Superieures, University of Montreal, 1986.
45. L. Valiant, V. Vazirani, NP is as easy as detecting unique solutions, Theoret. Comput. Sci. 47 (3) (1986) 85-93.
46. P. van Beek, Reasoning about qualitative temporal information, Artif. Intell. 58 (1992) 297-326.