Enhancing set constraint solvers with lexicographic bounds

Journal of Heuristics

Volumn 14, Issue 1, 2008, Pages 23-67

  Sadler, Andrew ^a   Gervet, Carmen ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Artificial intelligence; Constraint programming; Modelling languages

Indexed keywords

CONSTRAINT THEORY; MATHEMATICAL MODELS; MATHEMATICAL PROGRAMMING; PROBLEM SOLVING;

CONSTRAINT PROGRAMMING LITERATURE; FINITE SET (FS) CONSTRAINT SOLVERS; LEXICOGRAPHIC BOUNDS;

SET THEORY;

EID: 37649021366     PISSN: 13811231     EISSN: 15729397     Source Type: Journal    
DOI: 10.1007/s10732-007-9028-0     Document Type: Article

References (53)

1. Azevedo, F.: Constraint solving over multi-valued logics. Application to digital circuits. In: Frontiers in Artificial Intelligence and Applications. IOS, Amsterdam (2003)
2. Azevedo, F., Barahona, P.: Modeling digital circuits problems with set constraints. In: Lloyd, J., et al. (eds.) Computational Logic-CL (2000). Lecture Notes in Computer Science, vol. 1861, pp. 414-428. Springer, Berlin (2000)
3. Barnier, N., Brisset, P.: Facile: a functional constraint library. In: CICLOPS'01 Workshop, held alongside with CP-2001, 2001
4. Barnier, N., Brisset, P.: Solving the Kirkman's schoolgirl problem in a few seconds. In: Wallace, M. (ed.) Proceedings of CP-2004. Lecture Notes in Computer Science, vol. 3258. Springer, Berlin (2004)
5. Benhamou, F.: Interval constraint logic programming. In: Podelski, A. (ed.) Constraint Programming: Basics and Trends. Lecture Notes in Computer Science, vol. 910, pp. 11-12. Springer, Berlin (1995)
6. Berge, C.: Principles of Combinatorics. Academic, New York (1971)
7. Bessière, C., Hnich, B., Hébrard, E., Walsh, T.: Disjoint, partition and intersection constraints for sets and multiset variables. In: Wallace, M. (ed.) Proceedings of CP-2004. Lecture Notes in Computer Science, vol. 3258. Springer, Berlin (2004a)
8. Bessière, C., Hnich, B., Hébrard, E., Walsh, T.: The tractability of global constraints. In: Wallace, M. (ed.) Proceedings of CP-2004. Lecture Notes in Computer Science, vol. 3258. Springer, Berlin (2004b)
9. Bryant, R.E.: Symbolic Boolean manipulation with ordered binary-decision diagrams. ACM Comput. Surv. 24(3), 293-318 (1992)
10. Campbell, R.: A minimum distances basketball scheduling problem (1976)
11. Colbourn, C.J., Dinitz, J.H. (eds.): The CRC Handbook of Combinatorial Designs. CRC Press, Boca Raton (1998)
12. Colbourn, C.J., Dinitz, J.H., Stinson: Applications of combinatorial designs to communications, cryptography, and networking. In: Surveys in Combinatorics. London Mathematical Society Lecture Note Series, vol. 187. Cambridge University Press, Cambridge (1999)
13. Crawford, J., Ginsberg, M., Luks, E.M., Roy, A.: Symmetry breaking predicates for search problems. In: Fifth Int. Conf. on Knowledge Rep. and Reasoning, 1996
14. Eremin, A., Ajili, F., Rodosek, R.: A Set-based approach to the optimal IGP weight setting problem. In: Proceedings of INOC-2005 (2005)
15. Fahle, T., Schamberger, S., Sellman, M.: Symmetry breaking. In: Proceedings of CP'01, pp. 93-107. Springer, Berlin (2001)
16. Flener, P., Frisch, A., Hnich, B., Kiziltan, Z., Miguel, I., Pearson, J., Walsh, T.: Breaking row and column symmetries in matrix models. In: Proceedings of CP02. Springer, Berlin (2002)
17. Gent, I.P., Prosser, P., Smith, B.M.: A 0/1 encoding of the gaclex for pairs of vectors. In: ECAI-W9 Modelling and Solving Problems with Constraints (2002)
18. Gervet, C.: Conjunto: constraint logic programming with finite set domains. In: Bruynooghe, M. (ed.) Proceedings of ILPS-1994
19. Gervet, C.: Set intervals in constraint logic programming: definition and implementation of a language. Ph.D. thesis, Université de Franche-Comté, France (September 1995). European thesis (in English)
20. Gervet, C.: Interval propagation to reason about sets: definition and implementation of a practical language. Constraints J. 1(3), (1997)
21. Godsil, C.D.: Linear algebra and designs. Manuscript (229 p.) (1995)
22. Hawkins, P., Lagoon, V., Stuckey, P.: Solving set constraint satisfaction problems using ROBDDs. J. Artif. Intell. Res. 24 (2005)
23. Hnich, B., Kiziltan, Z., Walsh, T.: Combining symmetry breaking with other constraints: lexicographic ordering with sums. In: Proceedings of SymCon Workshop Held alongside CP'03, 2003
24. Holzbaur, C., Metastructures versus attributed variables in the context of extensible unification. In: Bruynooghe, M., Wirsing, M. (eds.) Proceedings of PLILP'92. Lecture Notes in Computer Science, vol. 631. Springer, Berlin (1992)
25. Ilog: User's manual. ILOG Solver 6.0 (September 2003)
26. Le Huitouze, S.: A new datastructure for implementing extensions to prolog. In: Proceedings of PLILP-1990. Lecture Notes in Computer Science, vol. 456. Springer, Berlin (1990)
27. Kiziltan, Z.: Symmetry breaking ordering constraints. Ph.D. thesis, Uppsala University, Sweden (2004)
28. Laburthe, F.: CHOCO: implementing a CP kernel. In: Proceedings of TRICS, held alongside CP-2000, http://choco.sourceforge.net/ (2000)
29. Lagoon, V., Stuckey, P.J.: Set domain propagation using ROBDDs. In: Wallace, M. (ed.) Proceedings CP-2004. Lecture Notes in Computer Science, vol. 3258. Springer, Berlin (2004)
30. Lee, J.H.M., van Emden, H.: Interval computation as deduction in CHIP. J. Logic Program. 16(34), 255-276 (1993)
31. Lindner, C.C., Rosa, A.: Topics on Steiner Systems. Annals of Discrete Mathematics, vol. 7. North-Holland, Amsterdam (1980)
32. Liu, H., Tobagi, F.: A novel efficient technique for traffic grooming in WDM SONET with multiple line speeds. In: Proceedings of IEEE ICC (2004)
33. Mackworth, A.K.: Consistency in networks of relations. Artif. Intell. (1977)
34. Mozart/Oz, http://www.mozart-oz.org/ (2004)
35. Müller, T.: Solving set partitioning problems with constraint programming. In: Proceedings of PAPPACT-1998 (1998)
36. Müller, T., Müller, M.: Finite set constraints in Oz. In: Bry, F., et al. (eds.) 13 Workshop Logische Programmierung (WLP '97). Technical Report 13, Technical University of Munich, Munich (1997)
37. Older, W., Vellino, A.: Constraint arithmetic on real intervals. In: Benhamou, F., Colmerauer, A. (eds.) Constraint Logic Programming: Selected Papers. MIT, Cambridge (1993)
38. Puget J.-F.: PECOS: a high level constraint programming language. In: Proceedings of Spicis (1992)
39. Puget, J.-F.: A fast algorithm for the bound consistency of alldiff constraints. In: Proceedings of AAAI'98 (1998)
40. Quimper, C.-G., Lopez-Ortiz, A., van Beek, P., Golynski, A.: Improved algorithms for the global cardinality constraint. In: Wallace, M. (ed.) Proceedings CP-2004. Lecture Notes in Computer Science, vol. 3258. Springer, Berlin (2004)
41. Sadler, A.: Strengthening finite set constraint solvers through active use of problem structure, symmetries and cardinality information. Ph.D. thesis, University of London, Imperial College (2005)
42. Sadler, A., Gervet, C.: Global reasoning on sets. In: FORMUL'01 Workshop on Modelling and Problem Formulation held alongside CP-2001, Paphos, Cyprus (2001)
43. Sadler, A., Gervet, C.: Global filtering for the disjointness constraint on fixed cardinality sets. Technical report ICPARC-04-02 (March 2004)
44. Sadler, A., Gervet, C.: Hybrid set domains to strengthen constraint propagation and reduce symmetries. In: Wallace, M. (ed.) Proceedings of CP-2004. Lecture Notes in Computer Science. Springer, Berlin (2004)
45. e : Technical report 03-1, IC-Parc, Imperial College, London (2003)
46. Sellman, M., van Hentenryck, P.: Structural symmetry breaking. In: Proceedings of IJCAI'05, Edinburgh, UK (2005)
47. Sherali, H.D., Smith, J.C.: Improving discrete model representations via symmetry considerations. Manag. Sci. 47, 1396-1407 (2001)
48. Smith, B.M.: Search strategies for optimization: modelling the sonet problem. In: 2nd International Workshop on Reformulating CSPs, 2003
49. Smith, B.M.: Symmetry and search in a network design problem. In: Proceedings of CP'AI-OR'05. Lecture Notes in Computer Science, vol. 3524. Springer, Berlin (2005)
50. Smith, J.C.: Tight discrete formulations to enhance solvability with applications to production, telecommunications and air transportation problems. Ph.D. thesis, Blacksburg, Virginia (2000)
51. Somenzi, F.: CUDD: Colorado University decision diagram package. http://vlsi.colorado.edu/~fabio/CUDD/ (2005)
52. Walsh, T.: Consistency and propagation with multiset constraints: a formal viewpoint. In: Proceedings of CP-2003. Lecture Notes in Computer Science. Springer, Berlin (2003)
53. Zhou, N.F.: B-Prolog. http://www.probp.com/ (2004)