Abstract
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 fixed-parameter tractable with respect to this parameter. © 2008 Springer-Verlag Berlin Heidelberg.
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CITATION STYLE
Hebrard, E., O’Sullivan, B., & Razgon, I. (2008). A soft constraint of equality: Complexity and approximability. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5202 LNCS, pp. 358–371). https://doi.org/10.1007/978-3-540-85958-1_24
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