Modularity-based decompositions for valued CSP
This paper addresses combinatorial problems that can be expressed as Valued Constraint Satisfaction Problems (VCSPs). In the VCSP framework, the constraints are defined by valuation functions to reflect several constraint violation levels. Despite the NP-hardness of VCSPs, tractable versions can be obtained by forcing the allowable valuation functions to have specific mathematical properties. This is the case of VCSPs with submodular valuation functions only. In this paper, we propose a problem decomposition scheme for binary VCSPs that takes advantage of modular valuation functions even when the studied problem is not limited to these functions. Modular functions are less frequent than submodular ones but, in compensation, they are easier to process. The proposed scheme works within a backtrack-based search and consists in decomposing the original problem into a set of modular, and then tractable, subproblems. Our decomposition scheme is distinguished by the possibility of instantiating variables by assigning to them subsets of values instead of single values.
combinatorial problems modular valuation functions problem decomposition scheme binary valued csps tractable subproblem