Constraint Programming pp 51-74 | Cite as

# Exploiting Structure in Constraint Satisfaction Problems

## Abstract

*Constraint satisfaction problems (CSPs)* involve finding values for problem variables subject to restrictions on which combinations of values are allowed. Fig. 2.1a presents an example: color the graph shown such that no vertices joined by an edge have the same color. The small letters indicate the choice of colors available at each vertex (a stands for aquamarine if you like). Here the variables are the vertices, the values for each variable are the set of colors available at the vertex and the constraints all happen to be the same: “not same color”. This is a *binary CSP* because all constraints involve two variables. For simplicity, we will assume here that our problems are presented as binary CSPs.

## Keywords

Search Tree Constraint Satisfaction Problem Conjunctive Search Constraint Graph Constraint Check## Preview

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## References

- Collin, Z., Dechter, R. and Katz, S. (1991) On the feasability of distributed constraint satisfaction.
*Proceedings of the Twelfth International Joint Conference on Artificial Intelligence*, 318–324Google Scholar - Cooper, M.O (1989) An optimal k-consistency algorithm.
*Artificial Intelligence*41, 89–95.MathSciNetCrossRefMATHGoogle Scholar - Dechter, R. (1990) Enhancement schemes for constraint processing: backjumping, learning and cutset decomposition.
*Artificial Intelligence*41, 273–312MathSciNetCrossRefGoogle Scholar - Dechter, R. and Pearl, J. (1988) Network-based heuristics for constraint-satisfaction problems.
*Artificial Intelligence*34, 1–38MathSciNetCrossRefGoogle Scholar - Dechter, R. and Pearl, J. (1989) Tree-clustering schemes for constraint-processing.
*Artificial Intelligence*38, 353–366MathSciNetCrossRefMATHGoogle Scholar - Freuder, E.C. (1982) A sufficient condition for backtrack-free search.
*Journal of the ACM*29, 24–32MathSciNetCrossRefMATHGoogle Scholar - Freuder, E.C. (1985) A sufficient condition for backtrack-bounded search.
*Journal of the ACM*32, 755–761MathSciNetCrossRefMATHGoogle Scholar - Freuder, E.C. (1988) Backtrack-free and backtrack-bounded search. In: L. Kanal, V. Kumar (eds.)
*Search in Artificial Intelligence*, 343–369. New York, Springer-VerlagCrossRefGoogle Scholar - Freuder, E.C. (1990) Complexity of k-tree structured constraint satisfaction problems.
*Proceedings of the Eighth National Conference on Artificial Intelligence*, 4–9Google Scholar - Freuder, E.C. (1991) Completable representations of constraint satisfaction problems.
*Proceedings of the Second International Conference on Principles of Knowledge Representation and Reasoning*, 186–195Google Scholar - Freuder, E.C. (1991). Eliminating interchangeable values in constraint satisfaction problems.
*Proceedings of the Ninth National Conference on Artificial Intelligence*, 227–233Google Scholar - Freuder, E.C. and Hubbe, P.D. (1993) Using inferred disjunctive constraints to decompose constraint satisfaction problems.
*Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence*, 254–260Google Scholar - Freuder, E.C. and Quinn, M.J. (1985) Taking advantage of stable sets of variables in constraint satisfaction problems.
*Proceedings of the Ninth International Joint Conference on Artificial Intelligence*, 1076–1078Google Scholar - Haselbock, A. (1993) Exploiting interchangeabilities in constraint satisfaction problems.
*Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence*, 282–287Google Scholar - Hubbe, P.D. and Freuder, E.C. (1992) An efficient cross product representation of the constraint satisfaction problem search space.
*Proceedings of The Tenth National Conference on Artificial Intelligence*, 421–427Google Scholar - Jegou, P. (1993) On the consistency of general constraint satisfaction problems.
*Proceedings of the Eleventh National Conference on Artificial Intelligence*, 114–119Google Scholar - Kirousis, L.M. and Thilikos, D.M. (1993)
*The linkage of a graph. Technical Report 93.04.16*, Computer Technology Institute, P.O Box 1122, Patras, GreeceGoogle Scholar - Lesaint, D. (1993) Specific sets of solutions for constraint satisfaction problems. Thirteenth International Conference on Expert Systems and Natural Language,
*Avignon*93, 255–264.Google Scholar - Mackworth, A.K. and Freuder, E.C. (1985) The complexity of some polynomial network consistency algorithms for constraint satisfaction problems.
*Artificial Intelligence*25, 65–74CrossRefGoogle Scholar - Mackworth. A.K. and Freuder, E.C. (1993) The complexity of constraint satisfaction revisited.
*Artificial Intelligence*59, 57–62CrossRefGoogle Scholar - Meiri. I., Dechter, R. and Pearl, J. (1990) Tree decomposition with applications to constraint processing.
*Proceedings of the Eighth National Conference on Artificial Intelligence*, 10–16Google Scholar - Montanari, U. and Rossi, F. (1991) Constraint relaxation can be perfect.
*Artificial Intelligence*48, 143–170MathSciNetCrossRefMATHGoogle Scholar - Schiex, T. and Verfaillie, G (1993) Constraint relaxation can be perfect.
*Artificial Intelligence*48, 143–170.Google Scholar - Seidel, R. (1988) A new method for solving constraint satisfaction problems.
*Proceedings of the Seventh International Joint Conference on Artificial Intelligence*, 338–342Google Scholar - Zabih, R. (1990) Some applications of graph bandwidth to constraint satisfaction problems.
*Proceedings of the Eighth national Conference on Artificial Intelligence*, 46–51.Google Scholar