When Functional and Bijective Constraints Make a CSP Polynomial

Many works have been carried out to improve search efficiency in CSPs, but few of them treated the semantics of the constraints. In this paper, we expose some properties of two classes of constraints, functional and bijective constraints: we first present conditions under which arc and path consistencies are sufficient to guarantee the existence of a bactrack free solution; we then exhibit classes of polynomial problems, and finally we propose a new method of decomposition for problems containing functional or bijective constraints. An interesting point in this method is that the resolution complexity is known prior to the search.

[1]  Rina Dechter,et al.  Tree Clustering for Constraint Networks , 1989, Artif. Intell..

[2]  Philippe Jégou,et al.  Synthia: Assisted Design of Peptide Synthesis Plans , 1991 .

[3]  Robert E. Tarjan,et al.  Depth-First Search and Linear Graph Algorithms , 1972, SIAM J. Comput..

[4]  Ugo Montanari,et al.  Networks of constraints: Fundamental properties and applications to picture processing , 1974, Inf. Sci..

[5]  Rina Dechter,et al.  From Local to Global Consistency , 1990, Artif. Intell..

[6]  Philippe Jégou.  Cyclic-Clustering: A Compromise between Tree-Clustering and Cycle-Cutset Method for Improving Search Efficiency , 1990, ECAI.

[7]  Robert M. Haralick,et al.  Increasing Tree Search Efficiency for Constraint Satisfaction Problems , 1979, Artif. Intell..

[8]  Eugene C. Freuder.  Synthesizing constraint expressions , 1978, CACM.

[9]  J. D. Uiiman,et al.  Principles of Database Systems , 2004, PODS 2004.

[10]  Rina Dechter,et al.  Network-Based Heuristics for Constraint-Satisfaction Problems , 1987, Artif. Intell..

[11]  Peter van Beek,et al.  On the Minimality and Decomposability of Constraint Networks , 1992, AAAI.

[12]  Mark W. Perlin,et al.  Arc consistency for factorable relations , 1991, [Proceedings] Third International Conference on Tools for Artificial Intelligence - TAI 91.

[13]  Pascal Van Hentenryck,et al.  An Efficient Arc Consistency Algorithm for a Class of CSP Problems , 1991, IJCAI.

[14]  Thomas C. Henderson,et al.  Arc and Path Consistency Revisited , 1986, Artif. Intell..

[15]  C. Berge.  Graphes et hypergraphes , 1970 .

[16]  Gerald J. Sussman,et al.  Forward Reasoning and Dependency-Directed Backtracking in a System for Computer-Aided Circuit Analysis , 1976, Artif. Intell..

[17]  Mark W. Perlin.  Arc Consistency for Factorable Relations , 1992, Artif. Intell..

[18]  Jeffrey D. Ullman,et al.  Principles of Database Systems , 1980 .