The regulargcc matrix constraint

Authors:
Ronald de Haan;Nina Narodytska;Toby Walsh
Affiliations:
Technische Universität Wien, Austria;NICTA and University of NSW, Sydney, Australia;NICTA and University of NSW, Sydney, Australia
Venue:
AI'12 Proceedings of the 25th Australasian joint conference on Advances in Artificial Intelligence
Year:
2012

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Abstract

We study propagation of a global constraint that 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 2 values, just 4 states in the automaton, just 5 columns to the matrix, or restricting to limited classes of automata). We also prove that propagation is W[2]-hard when the problem is parameterized by the number of rows in the matrix. On the positive side, we identify several cases where propagation is fixed parameter tractable.