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CONSTRAINTS
2008

Minimization of Locally Defined Submodular Functions by Optimal Soft Arc Consistency

8 years 5 months ago
Minimization of Locally Defined Submodular Functions by Optimal Soft Arc Consistency
Submodular function minimization is a polynomially-solvable combinatorial problem. Unfortunately the best known general-purpose algorithms have high-order polynomial time complexity. In many applications the objective function is locally-defined in that it is the sum of cost functions (also known as soft or valued constraints) whose arities are bounded by a constant. We prove that every Valued Constraint Satisfaction Problem with submodular cost functions has an equivalent instance on the same constraint scopes in which the actual minimum value of the objective function is rendered explicit. Such an equivalent instance is the result of establishing optimal soft arc consistency and can hence be found by solving a linear program. From a practical point of view, this provides us with an alternative algorithm for minimizing locally-defined submodular functions. From a theoretical point of view, this brings to light a previously-unknown connection between submodularity and soft arc consist...
Martin C. Cooper
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2008
Where CONSTRAINTS
Authors Martin C. Cooper
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