Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Solving large-scale QAP problems in parallel with the search library ZRAM
Journal of Parallel and Distributed Computing - Special issue on irregular problems in supercomputing applications
Approximating the maximum quadratic assignment problem
Information Processing Letters
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Approximating Global Quadratic Optimization with Convex Quadratic Constraints
Journal of Global Optimization
An O(n4) Algorithm for the QAP Linearization Problem
Mathematics of Operations Research
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We obtain a number of results regarding the distribution of values of a quadratic function f on the set of n × n permutation matrices (identified with the symmetric group Sn) around its optimum (minimum or maximum). We estimate the fraction of permutations σ such that f(σ) lies within a given neighborhood of the optimal value of f and relate the optimal value with the average value of f over a neighborhood of the optimal permutation. We describe a natural class of functions (which includes, for example, the objective function in the Traveling Salesman Problem) with a relative abundance of near-optimal permutations. Also, we identify a large class of functions f with the property that permutations close to the optimal permutation in the Hamming metric of Sn tend to produce near optimal values of f (such is, for example, the objective function in the symmetric Traveling Salesman Problem). We show that for general f, just the opposite behavior may take place: an average permutation in the vicinity of the optimal permutation may be much worse than an average permutation in the whole group Sn.