High-Order Consistency in Valued Constraint Satisfaction

Authors:
Martin C. Cooper
Affiliations:
IRIT, University of Toulouse III, Toulouse, France 31062
Venue:
Constraints
Year:
2005

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Abstract

k-consistency operations in constraint satisfaction problems (CSPs) render constraints more explicit by solving size-k subproblems and projecting the information thus obtained down to low-order constraints. We generalise this notion of k-consistency to valued constraint satisfaction problems (VCSPs) and show that it can be established in polynomial time when penalties lie in a discrete valuation structure.A generic definition of consistency is given which can be tailored to particular applications. As an example, a version of high-order consistency (face consistency) is presented which can be established in low-order polynomial time given certain restrictions on the valuation structure and the form of the constraint graph.