Date of this Version
Department of Computer Science & Engineering, University of Nebraska-Lincoln, Technical Report, TR-UNL-CSE-2011-0014
Freuder and Elfe  introduced Neighborhood Inverse Consistency (NIC) as a local consistency property defined on the values in the variables’ domains of a Constraint Satisfaction Problem (CSP). Debruyne and Bessiere  showed that enforcing NIC on binary CSPs is ineffective on sparse graph and too costly on dense graphs. In this thesis, we propose Relational Neighborhood Inverse Consistency (RNIC), an extension of NIC defined as a local consistency property on the tuples of the relations of a CSP. We characterize RNIC for both binary and non-binary CSPs, and propose an algorithm for enforcing it whose complexity is bounded by the degree of the dual graph on which the algorithm is applied. We propose to reduce the computational cost of our algorithm by reformulating the dual graph of the CSP. We present two reformulation techniques and their combinations, and discuss their effects on the consistency property enforced by the algorithm. We also describe a selection policy for choosing an appropriate reformulation technique, tying together the various components of our approach, which we show to outperforms, in a statistically significant manner, other common approaches for solving benchmark problems. Finally, we study the effect of the structure of the dual graph on the ordering of the propagation queue of our algorithm when applied as a preprocessing step to backtrack search and also as a lookahead strategy during search. We conclude, empirically, that the most effective ordering is the one that follows the tree decomposition of the dual graph.