Maximum quadratic assignment problem: reduction from maximum label cover and LP-based approximation algorithm

Authors:
Konstantin Makarychev;Rajsekar Manokaran;Maxim Sviridenko
Affiliations:
IBM Thomas J. Watson Research Center, Yorktown Heights, NY;Princeton University, Princeton, NJ;IBM Thomas J. Watson Research Center, Yorktown Heights, NY
Venue:
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Year:
2010

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Abstract

We show that for every positive ε 0, unless NP ⊂ BPQP, it is impossible to approximate the maximum quadratic assignment problem within a factor better than 2log1-εn by a reduction from the maximum label cover problem. Then, we present an O(√n)-approximation algorithm for the problem based on rounding of the linear programming relaxation often used in the state of the art exact algorithms.