Soft arc consistency revisited

The Valued Constraint Satisfaction Problem (VCSP) is a generic optimization problem defined by a network of local cost functions defined over discrete variables. It has applications in Artificial Intelligence, Operations Research, Bioinformatics and has been used to tackle optimization problems in other graphical models (including discrete Markov Random Fields and Bayesian Networks). The incremental lower bounds produced by local consistency filtering are used for pruning inside Branch and Bound search. In this paper, we extend the notion of arc consistency by allowing fractional weights and by allowing several arc consistency operations to be applied simultaneously. Over the rationals and allowing simultaneous operations, we show that an optimal arc consistency closure can theoretically be determined in polynomial time by reduction to linear programming. This defines Optimal Soft Arc Consistency (OSAC). To reach a more practical algorithm, we show that the existence of a sequence of ...

• Type: Journal
• Year: 2010
• Where: AI
• Authors: Martin C. Cooper, Simon de Givry, M. Sanchez, Thomas Schiex, Matthias Zytnicki, T. Werner
• Keywords: AI 2010, Arc Consistency, Arc Consistency Operations, Artificial Intelligence, Soft Arc Consistency