Affiliation:
1. Université Paris-Est Marne-la-Vallée, France
2. University of Oxford, Oxford, United Kingdom
Abstract
We study the computational complexity of exact minimization of rational-valued discrete functions. Let Γ be a set of rational-valued functions on a fixed finite domain; such a set is called a
finite-valued constraint language
. The valued constraint satisfaction problem, VCSP(Γ), is the problem of minimizing a function given as a sum of functions from Γ. We establish a dichotomy theorem with respect to exact solvability for
all
finite-valued constraint languages defined on domains of
arbitrary
finite size.
We show that every constraint language Γ either admits a binary symmetric fractional polymorphism, in which case the basic linear programming relaxation solves any instance of VCSP(Γ) exactly, or Γ satisfies a simple hardness condition that allows for a polynomial-time reduction from Max-Cut to VCSP(Γ).
Funder
European Research Council under the European Community's Seventh Framework Programme
Royal Society University Research Fellowship
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Cited by
37 articles.
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