Abstract
Many combinatorial search problems can be expressed as ‘constraint satisfaction problems’, and this class of problems is known to be NP-complete in general. In this paper we investigate ‘disjunctive constraints’, that is, constraints which have the form of the disjunction of two constraints of specified types. We show that when the constraint types involved in the disjunction have a certain property, which we call ‘independence’, and when a certain restricted class of problems is tractable, then the class of all problems involving these disjunctive constraints is tractable. We give examples to show that many known examples of tractable constraint classes arise in this way, and derive new tractable classes which have not previously been identified.
Preview
Unable to display preview. Download preview PDF.
References
Cooper, M.C., Cohen, D.A., Jeavons, P.G., “Characterizing tractable constraints”, Artificial Intelligence 65, (1994), pp. 347–361.
Cooper, M.C., & Jeavons, P.G., “Tractable constraints on ordered domains”, Artificial Intelligence 79, (1995), pp. 327–339.
Dechter, R., & Pearl, J., “Structure identification in relational data”, Artificial Intelligence 58 (1992) pp. 237–270.
Dechter, R. & Pearl J. “Network-based heuristics for constraint-satisfaction problems”, Artificial Intelligence 34 (1988), pp. 1–38.
Freuder, E.C., “A sufficient condition for backtrack-bounded search”, Journal of the ACM 32 (1985) pp. 755–761.
Garey, M.R., & Johnson, D.S., Computers and intractability: a guide to NPcompleteness, Freeman, San Francisco, California, (1979).
Gyssens, M., Jeavons, P., Cohen, D., “Decomposing constraint satisfaction problems using database techniques”, Artificial Intelligence 66, (1994), pp. 57–89.
Jackson, T.H., Number Theory, Routledge and Kegan Paul, (1975).
Jeavons, P., Cohen D., Gyssens, M., “A unifying framework for tractable constraints”, In Proceedings 1st International Conference on Principles and Practice of Constraint Programming—CP '95 (Cassis, France, September 1995), Lecture Notes in Computer Science, 976, Springer-Verlag, Berlin/New York, 1995, pp. 276–291.
Jonsson, P. and Bäckström, C., “A Linear Programming Approach to Temporal Reasoning”, Proceedings of AAAI-96, (1996).
Khachian, L.G., “A polynomial time algorithm for linear programming”, Soviet Math. Dokl. 20, (1979) pp. 191–194.
Kirousis, L., “Fast parallel constraint satisfaction”, Artificial Intelligence 64, (1993), pp. 147–160.
Koubarakis, M., “Dense Time and Temporal Constraints with ≠”, In Principles of Knowledge Representation and Reasoning: Proceedings of the Third International Conference (KR'92), (Ed. B. Nebel, C. Rich and W. Swartout), Morgan Kaufmann, San Mateo, CA, (1992), pp. 24–35.
Koubarakis, M., “From Local to Global Consistency in Temporal Constraint Networks”, In Proceedings 1st International Conference on Principles and Practice of Constraint Programming-CP '95 (Cassis, France, September 1995), Lecture Notes in Computer Science, 976, Springer-Verlag, Berlin/New York, (1995), pp. 53–69.
Koubarakis, M., “Tractable Disjunctions of Linear Constraints”, In Proceedings of the 2nd International Conference on Principles and Practice of Constraint Programming-CP '96 (Boston, MA, August 1996), Lecture Notes in Computer Science, 1118, Springer-Verlag, Berlin/New York, (1996), pp. 297–307.
Ladkin, P.B., & Maddux, R.D., “On binary constraint problems”, Journal of the ACM 41 (1994), pp. 435–469.
Lassez, J-L., and McAloon, K., “A Canonical Form for Generalized Linear Constraints”, Technical Report RC15004 (#67009), IBM Research Division, T.J. Watson Research Center, (1989).
Lassez, J-L., and McAloon, K., “A Canonical Form for Generalized Linear Constraints”, Lecture Notes in Computer Science, 351, Springer-Verlag, Berlin/New York, (1989), pp. 19–27.
Mackworth, A.K. “Consistency in networks of relations”, Artificial Intelligence 8 (1977) pp. 99–118.
Montanari, U., “Networks of constraints: fundamental properties and applications to picture processing”, Information Sciences 7 (1974), pp. 95–132.
Montanari, U., & Rossi, F., “Constraint relaxation may be perfect”, Artificial Intelligence 48 (1991), pp. 143–170.
Nebel, B. & Burckert, H-J., “Reasoning about temporal relations: a maximal tractable subclass of Allen's interval algebra”, Journal of the ACM 42, (1995), pp. 43–66.
Schaefer, T.J., “The complexity of satisfiability problems”, Proc 10th ACM Symposium on Theory of Computing (STOC), (1978) pp. 216–226.
Tsang, E., Foundations of Constraint Satisfaction, Academic Press, (1993).
van Beek, P., “On the Minimality and Decomposability of Row-Convex Constraint Networks”, Proceedings of the Tenth National Conference on Artificial Intelligence, AAAI-92, MIT Press, (1992) pp. 447–452.
Van Hentenryck, P., Deville, Y., Teng, C-M., “A generic arc-consistency algorithm and its specializations”, Artificial Intelligence 57 (1992), pp. 291–321.
Vilain, M., Kautz, H., van Beek, P., “Constraint Propagation Algorithms for Temporal Reasoning: A Revised Report”, In Readings in Qualitative Reasoning about Physical Systems, Ed. Weld, D.S. and de Kleer, J., Morgan Kaufmann, (1989), pp. 373–381.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cohen, D., Jeavons, P., Koubarakis, M. (1997). Tractable disjunctive constraints. In: Smolka, G. (eds) Principles and Practice of Constraint Programming-CP97. CP 1997. Lecture Notes in Computer Science, vol 1330. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017461
Download citation
DOI: https://doi.org/10.1007/BFb0017461
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63753-0
Online ISBN: 978-3-540-69642-1
eBook Packages: Springer Book Archive