Approximating the minimum quadratic assignment problems

Refael Hassin, Asaf Levin, Maxim Sviridenko

Abstract: We consider the well-known minimum quadratic assignment problem. In this problem we are given two n × n nonnegative symmetric matrices A = (aij) and B = (bij). The objective is to compute a permutation π of V = {1,…,n} so that ∑ i,j∈Vi≠j aπ(i),π(j)bi,j is minimized. We assume that A is a 0/1 incidence matrix of a graph, and that B satisfies the triangle inequality. We analyze the approximability of this class of problems by providing polynomial bounded approximations for some special cases, and inapproximability results for other cases.