Using Auxiliary Variables and Implied Constraints to Model Non-Binary Problems

Barbara Smith, University of Leeds; Kostas Stergiou, University of Strathclyde; Toby Walsh, University of York

We perform an extensive theoretical and empirical analysis of the use of auxiliary variables and implied constraints in modelling a class of non-binary constraint satisfaction problems called problems of distance. This class of problems includes 1-d, 2-d and circular Golomb rulers. We identify a large number of different models, both binary and non-binary, and compare theoretically the level of consistency achieved by generalized arc consistency on them. Our experiments show that the introduction of auxiliary variables and implied constraints can significantly reduce the size of the search space. For instance, our final models reduce the time to find an optimal 10-mark Golomb ruler 50-fold.

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