Rainer E. Burkard

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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 uni ed testbed for QAP, accessible to the scienti c community. It consisted of(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)
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 polytope and the(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)
Burkard, R.E. and W. Sandholzer, Efficiently solvable special cases of bottleneck travelling salesman problems, Discrete Applied Mathematics 32 (1991) 61-76. The paper investigates bottleneck travelling salesman problems (BTSP) which can be solved in polynomial time. At first a BTSP whose cost matrix is a circulant is treated. It is shown that in the(More)