# An Algebraic Theory of Complexity for Discrete Optimization

@article{Cohen2013AnAT, title={An Algebraic Theory of Complexity for Discrete Optimization}, author={David A. Cohen and Martin C. Cooper and P{\'a}id{\'i} Creed and Peter Jeavons and Stanislav Živn{\'y}}, journal={SIAM J. Comput.}, year={2013}, volume={42}, pages={1915-1939} }

Discrete optimization problems arise in many different areas and are studied under many different names. In many such problems the quantity to be optimized can be expressed as a sum of functions of a restricted form. Here we present a unifying theory of complexity for problems of this kind. We show that the complexity of a finite-domain discrete optimization problem is determined by certain algebraic properties of the objective function, which we call weighted polymorphisms. We define a Galois…

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