Maximizing polynomials subject to assignment constraints

Authors:
Konstantin Makarychev;Maxim Sviridenko
Affiliations:
IBM Thomas J. Watson Research Center;IBM Thomas J. Watson Research Center
Venue:
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Year:
2011

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Abstract

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.