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A maximal tractable class of soft constraints.

Cohen, D. and Cooper, M. and Jeavons, P. and Krokhin, A. (2004) 'A maximal tractable class of soft constraints.', Journal of artificial intelligence research., 22 . pp. 1-22.


Many researchers in artificial intelligence are beginning to explore the use of soft constraints to express a set of (possibly conflicting) problem requirements. A soft constraint is a function defined on a collection of variables which associates some measure of desirability with each possible combination of values for those variables. However, the crucial question of the computational complexity of finding the optimal solution to a collection of soft constraints has so far received very little attention. In this paper we identify a class of soft binary constraints for which the problem of finding the optimal solution is tractable. In other words, we show that for any given set of such constraints, there exists a polynomial time algorithm to determine the assignment having the best overall combined measure of desirability. This tractable class includes many commonly-occurring soft constraints, such as 'as near as possible' or 'as soon as possible after', as well as crisp constraints such as 'greater than'. Finally, we show that this tractable class is maximal, in the sense that adding any other form of soft binary constraint which is not in the class gives rise to a class of problems which is NP-hard.

Item Type:Article
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Date accepted:No date available
Date deposited:07 April 2010
Date of first online publication:July 2004
Date first made open access:No date available

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