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    A soft constraint of equality: complexity and approximability

    Hebrard, E. and O’Sullivan, B. and Razgon, Igor (2008) A soft constraint of equality: complexity and approximability. In: Stuckey, P.J. (ed.) Principles and Practice of Constraint Programming. Lecture Notes in Computer Science 5202. Berlin, Germany: Springer Verlag, pp. 358-371. ISBN 9783540859581.

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    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.


    Item Type: Book Section
    School: Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
    Depositing User: Sarah Hall
    Date Deposited: 01 Aug 2013 16:06
    Last Modified: 09 Aug 2023 12:34


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