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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