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We show that for every positive e > 0, unless NP ⊂ BPQP, it is impossible to approximate the maximum quadratic assignment problem within a factor better than 2log1-en by a reduction from the maximum label cover problem. 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.

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