A Soft Constraint of Equality: Complexity and Approximability

We introduce the SoftAllEqual global 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 SoftAllEqual constraint is fixedparameter tractable with respect to this parameter.

• Type: Conference
• Year: 2008
• Where: CP
• Authors: Emmanuel Hebrard, Barry O'Sullivan, Igor Razgon
• Keywords: Artificial Intelligence, Computational Complexity, CP 2008, Greedy Linear-time Algorithm, SoftAllEqual Global Constraint