 
Summary: Approximating the Maximum Quadratic Assignment Problem 1
Esther M. Arkin 2 Refael Hassin 3 Maxim Sviridenko 4
Keywords: Approximation algorithm; quadratic assignment problem
1 Introduction
In the maximum quadratic assignment problem three n \Theta n nonnegative symmetric matrices
A = (a ij ), B = (b ij ), and C = (c ij ) are given and the objective is to compute a permutation ß of
V = f1; : : : ; ng so that
P
i;j2V
i6=j
a ß(i);ß(j) b i;j +
P
i2V c i;ß(i) is maximized.
The problem is NPhard and generalizes many NPhard problems such as max clustering
with given sizes (see definition below). An indication to the hardness of approximating the
problem is that the best known approximation factors for two special cases of max clustering
with given sizes are 1
c
, when all sizes are equal to a constant c [7], and (n) \Gamma 1
3 when all sizes
