Maximum Quadratic Assignment Problem: Reduction from Maximum Label Cover and LP-based Approximation Algorithm [article]

Konstantin Makarychev and Rajsekar Manokaran and Maxim Sviridenko
2014 arXiv   pre-print
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 2^^1-ϵ n by a reduction from the maximum label cover problem. Our result also implies that Approximate Graph Isomorphism is not robust and is in fact, 1 - ϵ vs ϵ hard assuming the Unique Games Conjecture. 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.
arXiv:1403.7721v1 fatcat:k3k4zelnazd55h2lakc4sibxfa