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arXiv · 1201.0564

The RegularGcc Matrix Constraint

Ronald de Haan·Nina Narodytska·Toby Walsh
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Abstract

We study propagation of the RegularGcc global constraint. This ensures that each row of a matrix of decision variables satisfies a Regular constraint, and each column satisfies a Gcc constraint. On the negative side, we prove that propagation is NP-hard even under some strong restrictions (e.g. just 3 values, just 4 states in the automaton, or just 5 columns to the matrix). On the positive side, we identify two cases where propagation is fixed parameter tractable. In addition, we show how to improve propagation over a simple decomposition into separate Regular and Gcc constraints by identifying some necessary but insufficient conditions for a solution. We enforce these conditions with some additional weighted row automata. Experimental results demonstrate the potential of these methods on some standard benchmark problems.

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Ronald de Haan, Nina Narodytska, Toby Walsh. 2012-01-03. The RegularGcc Matrix Constraint. https://arxiv.org/abs/1201.0564

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