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The complexity of finite-valued CSPs

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If you have a question about this talk, please contact Dr Thomas Sauerwald.

Let L be a set of rational-valued functions on a fixed finite domain; such a set is called a finite-valued constraint language. We are interested in the problem of minimising a function given explicitly as a sum of functions from L. We establish a dichotomy theorem with respect to exact solvability for all finite-valued languages defined on domains of arbitrary finite size. We present a simple algebraic condition that characterises the tractable cases. Moreover, we show that a single algorithm based on linear programming solves all tractable cases. Furthermore, we show that there is a single reason for intractability; namely, a very specific reduction from Max-Cut.

(based on work published at FOCS ’12 and STOC ’13, joint work with J.Thapper)

This talk is part of the Cambridge Algorithms talks series.

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