Cohen, D. and Cooper, M. and Jeavons, P. and Krokhin, A. (2005) 'Supermodular functions and the complexity of MAX CSP.', Discrete applied mathematics., 149 (1-3). pp. 53-72.
In this paper we study the complexity of the maximum constraint satisfaction problem (MAX CSP) over an arbitrary finite domain. An instance of MAX CSP consists of a set of variables and a collection of constraints which are applied to certain specified subsets of these variables; the goal is to find values for the variables which maximize the number of simultaneously satisfied constraints. Using the theory of sub- and supermodular functions on finite lattice-ordered sets, we obtain the first examples of general families of efficiently solvable cases of MAX CSP for arbitrary finite domains. In addition, we provide the first dichotomy result for a special class of non-Boolean MAX CSP, by considering binary constraints given by supermodular functions on a totally ordered set. Finally, we show that the equality constraint over a non-Boolean domain is non-supermodular, and, when combined with some simple unary constraints, gives rise to cases of MAX CSP which are hard even to approximate.
|Keywords:||Constraint satisfaction problem, Optimization, Supermodularity.|
|Full text:||Full text not available from this repository.|
|Publisher Web site:||http://dx.doi.org/10.1016/j.dam.2005.03.003|
|Record Created:||21 Feb 2008|
|Last Modified:||28 Apr 2009 12:04|
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