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

الأصل · EN

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 2¹⁻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.