Abstract
A constraint satisfaction problem involves finding values for variables subject to constraints on which combinations of values are allowed. In some cases it may be impossible or impractical to solve these problems completely. We may seek to partially solve the problem, in particular by satisfying a maximal number of constraints. Standard backtracking and local consistency techniques for solving constraint satisfaction problems can be adapted to cope with, and take advantage of, the differences between partial and complete constraint satisfaction. Extensive experimentation on maximal satisfaction problems illuminates the relative and absolute effectiveness of these methods. A general model of partial constraint satisfaction is proposed.
This paper is reprinted (with minor changes) from Artificial Intelligence, volume 58, numbers 1–3, E. C. Freuder and R. J. Wallace, Partial constraint satisfaction, pages 21–70, 1992 with kind permission from Elsevier Science — NL, Sara Burgerhartstraat 25, 1055 KV Amsterdam, The Netherlands. (This volume was a special issue that was reprinted as an MIT Press book, Constraint-Based Reasoning).
Preview
Unable to display preview. Download preview PDF.
References
D. A. Belsley, E. Kuh, and R. E. Welsch. Regression Diagnostics. Wiley, New York, NY, 1980.
A. Borning, R. Duisberg, B. Freeman-Benson, A. Kramer, and M. Woolf. Constraint hierarchies. In Proceedings 1987 ACM Conference on Object-Oriented Programming Systems, Languages and Applications, pages 48–60, 1987.
A. Borning, M. Maher, A. Martindale, and M. Wilson. Constraint hierarchies and logic programming. In Proceedings Sixth International Conference on Logic Programming, pages 149–164, 1989.
P. Cheesemen, B. Kanefsky, and W. M. Taylor. Where the really hard problems are. In Proceedings IJCAI-91, pages 331–337, 1991.
M. Cooper. Visual Occlusion and the Interpretation of Ambiguous Pictures. Ellis Horwood, Chicester, 1992.
R. Dechter. Enhancement schemes for constraint processing: backjumping, learning, and cutset decomposition. Artif. Intell., 41:273–312, 1990.
R. Dechter, A. Dechter, and J. Pearl. Optimization in constraint networks. In R. M. Oliver and J. Q. Smith, editors, Influence Diagrams, Belief Nets and Decision Analysis, pages 411–425. Wiley, 1990.
R. Dechter and J. Pearl. Network-based heuristics for constraint satisfaction problems. Artif. Intell., 34:1–38, 1988.
R. Dechter and J. Pearl. Tree-clusstering schemes for constraint processing. Artif. Intell., 38:353–366, 1989.
Y. Descotte and J. C. Latombe. Making compromises among antagonistic constraints in a planner. Artif. Intell., 27:183–217, 1985.
R. Feldman and M. C. Golumbic. Optimization algorithms for student scheduling via constraint satisfiability. Comput. J., 33:356–364, 1990.
M. Fox. Constraint-directed Search: A Case Study of Job-Shop Scheduling. Morgan Kaufmann, Los Altos, CA, 1987.
E. C. Freuder. Backtrack-free and backtrack-bounded search. In L. Kanal and V. Kumar, editors, Search in Artificial Intelligence, pages 343–369. Springer, New York, NY, 1988.
E. Freuder. Partial constraint satisfaction. In Proceedings IJCAI-89, pages 278–283, 1989.
E. Freuder. Complexity of k-tree structured constraint satisfaction problems. In Proceedings AAAI-90, pages 4–9, 1990.
J. Gaschnig. A general backtrack algorithm that elimates most redundant checks. In Proceedings IJCAI-77, page 457, 1977.
J. Gaschnig. Experimental case studies of backtrack vs. Waltz-type vs. new algorithms for satisficing assignment problems. In Proceedings Second National Conference of the Canadian Society for Computational Studies of Intelligence, pages 268–277, 1978.
S. W. Golumb and L. D. Baumert. Backtrack programming. J. ACM, 12:516–524, 1965.
R.M. Haralick and G.L. Elliott. Increasing tree search efficiency for constraint satisfaction problems. Artificial Intelligence, 14:263–313, 1980.
W. Hower. Sensitive relaxation of an overspecified constraint network. In Proceedings Second International Symposium on Artificial Intelligence, 1989.
S. Huard and E. Freuder. A debugging assistant for incompletely specified constraint network knowledge bases. Int. J. Expert Syst.: Res. Appl., pages 419–446, 1993.
R. E. Kirk. Experimental Design. Brooks/Cole, Pacific Grove, CA, 2nd edition, 1982.
V. Kumar. Algorithms for constraint-satisfaction problems: a survey. AI Mag., 13:32–44, 1992.
M. Lacroix and P. Lavency. Preferences: putting more knowledge into queries. In Proceedings 15th International Conference on Very Large Data Bases, pages 217–225, 1987.
E. L. Lawler and D. E. Wood. Branch-and-bound methods: a survey. Oper. Res., 14:699–719, 1966.
A. Mackworth. Consistency in networks of relations. Artif. Intell., 8:99–118, 1977.
A. Mackworth and E. Freuder. The complexity of some polynomial network consistency algorithms of constraint satisfaction problems. Artif. Intell., 25:65–74, 1985.
I. Meiri, R. Dechter, and J. Pearl. Tree decomposition with applications to constraint processing. In Proceedings AAAI-90, pages 10–16, 1990.
P. Meseguer. Constraint satisfaction problems: an overview. AI Commun., 2:3–17, 1989.
S. Mittal and B. Falkenhainer. Dynamic constraint satisfaction problems. In Proceedings AAAI-90, pages 25–32, 1990.
R. Mohr and G. Masini. Good old discrete relaxation. In Proceedings European Conference on Artificial Intelligence, pages 651–656, 1988.
B. Nadel. Constraint satisfaction algorithms. Comput. Intell., 5:188–224, 1989.
E. M. Reingold, J. Nievergelt, and N. Deo. Combinatorial Algorithms: Theory and Practice. Prentice-Hall, Englewood Cliffs, NJ, 1977.
A. Rosenfeld, R. Hummel, and S. Zucker. Scene labeling by relaxation operations. IEEE Trans. Syst. Man, Cybern., 6:420–433, 1976.
L. Shapiro and R. Haralick. Structural descriptions and inexact matching. IEEE Trans. Patt. Anal. Mach. Intell., 3:504–519, 1981.
P. Snow and E. Freuder. Improved relaxation and search methods for approximate constraint satisfaction with a maximin criterion. In Proceedings Eighth Biennial Conference of the Canadian Society for Computational Studies of Intelligence, pages 227–230, 1990.
P. Van Hentenryck. Constraint Satisfaction in Logic Programming. MIT, Cambridge, MA, 1989.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Freuder, E.C., Wallace, R.J. (1996). Partial constraint satisfaction. In: Jampel, M., Freuder, E., Maher, M. (eds) Over-Constrained Systems. OCS 1995. Lecture Notes in Computer Science, vol 1106. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61479-6_18
Download citation
DOI: https://doi.org/10.1007/3-540-61479-6_18
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61479-1
Online ISBN: 978-3-540-68601-9
eBook Packages: Springer Book Archive