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 2 log 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 versus 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 state-of-the-art exact algorithms.
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