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The Quadratic Assignment Problem (QAP) has remained one of the great challenges in combinatorial optimization. It is still considered a computationally nontrivial task to solve modest size problems, say of size n = 20: The QAPLIB was rst published in 1991, in order to provide a uniied testbed for QAP, accessible to the scientiic community. It consisted of… (More)

Page 55 line 6: replace " among the matched " with " among the unmatched " ; 229 line 13: replace " Palubeckis [544] " with the following (missing) reference: G. Palubeckis. The use of special graphs for obtaining lower bounds in the geometric quadratic assignment problem. 289 eqn (9.27): replace " s ∈ F " with " S ∈ F " ; 308 line 14: replace "… (More)

This paper aims at describing the state of the art on quadratic assignment problems (QAPs). It discusses the most important developments in all aspects of the QAP such as linearizations, QAP polyhedra, algorithms to solve the problem to optimality, heuristics, polynomially solvable special cases, and asymptotic behavior. Moreover, it also considers problems… (More)

Given three n-element sequences a i ; b i and c i of nonnega-tive real numbers, the aim is to nd two permutations and such that the sum P n i=1 a i b (i) c (i) is minimized (maximized, respectively). We show that the maximization version of this problem can be solved in polynomial time, whereas we present an NP-completeness proof for the minimization… (More)

Let us denote a ⊕ b = max(a; b) and a ⊗ b = a + b for a; b ∈ R = R ∪ {−∞} and extend this pair of operations to matrices and vectors in the same way as in linear algebra. We present an O(n 2 (m + n log n)) algorithm for ÿnding all essential terms of the max-algebraic characteristic polynomial of an n × n matrix over R with m ÿnite elements. In the cases… (More)

This paper aims at describing the state of the art on linear assignment problems (LAPs). Besides sum LAPs it discusses also problems with other objective functions like the bottleneck LAP, the lexicographic LAP, and the more general algebraic LAP. We consider different aspects of assignment problems, starting with the assignment poly-tope and the… (More)