Maximizing Polynomials Subject to Assignment Constraints

We study the q-adic assignment problem. We first give an O(n(q−1)/2))-approximation algorithm for the Koopmans--Beckman version of the problem, improving upon the result of Barvinok. Then, we introduce a new family of instances satisfying “tensor triangle inequalities” and give a constant factor approximation algorithm for them. We show that many classical optimization problems can be modeled by q-adic assignment problems from this family. Finally, we give several integrality gap examples for the natural LP relaxations of the problem.

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