Detecting Unsatisfiable CSPs by Coloring the Micro-Structure

Constraint satisfaction research has focussed on consistency checking using k-consistency ilnd its variations such as arc-consistency, and path-consistency. We define a new form of consistency checking that is based on coloring the micro-structure graph of a constraint satisfaction problem (CSP). In our formulation, if the micro-structure graph of a CSP with n variables can be colored with n - 1 colors then the problem is unsatisfiable. This new notion of consistency-by-coloring is compared to arc-consistency. We provide examples that show that neither arc-consistency. nor consistency-by-coloring is more powerful than the other in a theoretical sense. We also describe the results of preliminary computational experiments that compare consistency-by-coloring and arc-consistency.

[1]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[2]  Pascal Van Hentenryck,et al.  A Generic Arc-Consistency Algorithm and its Specializations , 1992, Artif. Intell..

[3]  Philippe Jégou.  Decomposition of Domains Based on the Micro-Structure of Finite Constraint-Satisfaction Problems , 1993, AAAI.

[4]  Thomas Schiex,et al.  Lazy Arc Consistency , 1996, AAAI/IAAI, Vol. 1.

[5]  Alan K. Mackworth.  Consistency in Networks of Relations , 1977, Artif. Intell..

[6]  C. Bessiere,et al.  An arc-consistency algorithm optimal in the number of constraint checks , 1994, Proceedings Sixth International Conference on Tools with Artificial Intelligence. TAI 94.

[7]  Eugene C. Freuder.  Using Metalevel Constraint Knowledge to Reduce Constraint Checking , 1995, Constraint Processing, Selected Papers.

[8]  Jean-Charles Régin,et al.  A Filtering Algorithm for Constraints of Difference in CSPs , 1994, AAAI.

[9]  John N. Hooker,et al.  Testing heuristics: We have it all wrong , 1995, J. Heuristics.

[10]  Barbara M. Smith,et al.  The Phase Transition and the Mushy Region in Constraint Satisfaction Problems , 1994, ECAI.

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

[12]  Daniel Brélaz,et al.  New methods to color the vertices of a graph , 1979, CACM.

[13]  Toby Walsh,et al.  The Constrainedness of Search , 1996, AAAI/IAAI, Vol. 1.

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

[15]  Eugene C. Freuder,et al.  Contradicting Conventional Wisdom in Constraint Satisfaction , 1994, ECAI.

[16]  Christian Bessiere,et al.  Arc-Consistency and Arc-Consistency Again , 1993, Artif. Intell..