A Soft Constraint of Equality: Complexity and Approximability

Authors:
Emmanuel Hebrard;Barry O'Sullivan;Igor Razgon
Affiliations:
Cork Constraint Computation Centre Department of Computer Science, University College Cork, Ireland;Cork Constraint Computation Centre Department of Computer Science, University College Cork, Ireland;Cork Constraint Computation Centre Department of Computer Science, University College Cork, Ireland
Venue:
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
Year:
2008

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Abstract

We introduce the SoftAllEqualglobal constraint, which maximizes the number of equalities holding between pairs of assignments to a set of variables. We study the computational complexity of propagating this constraint, showing that it is intractable in general, since maximizing the number of pairs of equally assigned variables in a set is NP-hard. We propose three ways of coping with NP-hardness. Firstly, we develop a greedy linear-time algorithm to approximate the maximum number of equalities within a factor of 2. Secondly, we identify a tractable (polynomial) class for this constraint. Thirdly, we identify a parameter based on this class and show that the SoftAllEqualconstraint is fixed-parameter tractable with respect to this parameter.