The hardness of approximation: gap location
Computational Complexity
Approximation algorithms for minimum tree partition
Discrete Applied Mathematics
Approximation algorithms for min-sum p-clustering
Discrete Applied Mathematics
P-Complete Approximation Problems
Journal of the ACM (JACM)
Approximating the maximum quadratic assignment problem
Information Processing Letters
Approximation algorithms
Approximation algorithms for maximization problems arising in graph partitioning
Journal of Algorithms
SIAM Journal on Discrete Mathematics
Collective annotation of Wikipedia entities in web text
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
Approximating the minimum quadratic assignment problems
ACM Transactions on Algorithms (TALG)
A Fourier space algorithm for solving quadratic assignment problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
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Quadratic Assignment is a basic problem in combinatorial optimization, which generalizes several other problems such as Traveling Salesman, Linear Arrangement, Dense k Subgraph, and Clustering with given sizes. The input to the Quadratic Assignment Problem consists of two n x n symmetric non-negative matrices W = (wi, j) and D = (di, j). Given matrices W, D, and a permutation π: [n] → [n], the objective function is [EQUATION]. In this paper, we study the Maximum Quadratic Assignment Problem, where the goal is to find a permutation π that maximizes Q(π). We give an Õ(√n) approximation algorithm, which is the first non-trivial approximation guarantee for this problem. The above guarantee also holds when the matrices W, D are asymmetric. An indication of the hardness of Maximum Quadratic Assignment is that it contains as a special case, the Dense k Subgraph problem, for which the best known approximation ratio ≈ n1/3 (Feige et al. [8]). When one of the matrices W, D satisfies triangle inequality, we obtain a [EQUATION] approximation algorithm. This improves over the previously bestknown approximation guarantee of 4 (Arkin et al. [4]) for this special case of Maximum Quadratic Assignment. The performance guarantee for Maximum Quadratic Assignment with triangle inequality can be proved relative to an optimal solution of a natural linear programming relaxation, that has been used earlier in Branch-and-Bound approaches (see eg. Adams and Johnson [1]). It can also be shown that this LP has an integrality gap of [EQUATION] for general Maximum Quadratic Assignment.