Maximum Quadratic Assignment Problem: Reduction from Maximum Label Cover and LP-Based Approximation Algorithm

Konstantin Makarychev, Rajsekar Manokaran, Maxim Sviridenko

Abstract: We show that for every positive ε> 0, unless ${\mathcal NP} \subset {\mathcal BPQP}$ , it is impossible to approximate the maximum quadratic assignment problem within a factor better than $2^{\log^{1-\varepsilon} n}$ by a reduction from the maximum label cover problem. Then, we present an $O(\sqrt{n})$ -approximation algorithm for the problem based on rounding of the linear programming relaxation often used in the state of the art exact algorithms.