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The Quadratic Assignment Problem
 HANDBOOK OF COMBINATORIAL OPTIMIZATION, P. PARDALOS AND D.Z. DU, EDS.
, 1998
"... 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, an ..."
Abstract

Cited by 107 (3 self)
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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 related to the QAP, e.g. the biquadratic assignment problem, and discusses the relationship between the QAP and other well known combinatorial optimization problems, e.g. the traveling salesman problem, the graph partitioning problem, etc. The paper will appear in the Handbook of Combinatorial Optimization to be published by Kluwer Academic Publishers, P. Pardalos and D.Z. Du, eds.
Frequency Assignment Problems
 HANDBOOK OF COMBINATORIAL OPTIMIZATION
, 1999
"... The ever growing number of wireless communications systems deployed around the globe have made the optimal assignment of a limited radio frequency spectrum a problem of primary importance. At issue are planning models for permanent spectrum allocation, licensing, regulation, and network design. Furt ..."
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Cited by 30 (3 self)
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The ever growing number of wireless communications systems deployed around the globe have made the optimal assignment of a limited radio frequency spectrum a problem of primary importance. At issue are planning models for permanent spectrum allocation, licensing, regulation, and network design. Further at issue are online algorithms for dynamically assigning frequencies to users within an established network. Applications include aeronautical mobile, land mobile, maritime mobile, broadcast, land fixed (pointto point), and satellite systems. This paper surveys research conducted by theoreticians, engineers, and computer scientists regarding the frequency assignment problem (FAP) in all of its guises. The paper begins by defining some of the more common types of FAPs. It continues with a discussion on measures of optimality relating to the use of spectrum, models of interference, and mathematical representations of the many FAPs, both in graph theoretic terms, and as mathematical pro...
Selected Topics on Assignment Problems
, 1999
"... We survey recent developments in the fields of bipartite matchings, linear sum assignment and bottleneck assignment problems and applications, multidimensional assignment problems, quadratic assignment problems, in particular lower bounds, special cases and asymptotic results, biquadratic and co ..."
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Cited by 22 (1 self)
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We survey recent developments in the fields of bipartite matchings, linear sum assignment and bottleneck assignment problems and applications, multidimensional assignment problems, quadratic assignment problems, in particular lower bounds, special cases and asymptotic results, biquadratic and communication assignment problems.
An Asymptotical Study of Combinatorial Optimization Problems By Means of Statistical Mechanics
, 1998
"... . The analogy between combinatorial optimization and statistical mechanics has proven to be a fruitful object of study. Simulated annealing, a metaheuristic for combinatorial optimization problems, is based on this analogy. In this paper we use the statistical mechanics formalism based on the above ..."
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Cited by 5 (2 self)
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. The analogy between combinatorial optimization and statistical mechanics has proven to be a fruitful object of study. Simulated annealing, a metaheuristic for combinatorial optimization problems, is based on this analogy. In this paper we use the statistical mechanics formalism based on the above mentioned analogy to analyze the asymptotic behavior of a special class of combinatorial optimization problems characterized by a combinatorial conditions which is well known in the literature. Our result is analogous to results of other authors derived by purely probabilistic means: Under natural probabilistic conditions on the coefficients of the problem, the ratio between the optimal value and size of a feasible solution approaches almost surely the expected value of the coefficients, as the size of the problem tends to infinity. Our proof shows clearly why the above mentioned combinatorial condition which characterizes the class of investigated problems is essential. Keywords: combinato...
A NOTE ON THE ASYMPTOTIC BEHAVIOUR OF BOTTLENECK PROBLEMS
"... Abstract. We generalize and sharpen results of Burkard and Fincke concerning the asymptotic behaviour of a certain class of combinatorial optimization problems with bottleneck objective function. In this way several open questions are answered. 1. ..."
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Cited by 2 (0 self)
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Abstract. We generalize and sharpen results of Burkard and Fincke concerning the asymptotic behaviour of a certain class of combinatorial optimization problems with bottleneck objective function. In this way several open questions are answered. 1.
The quadratic assignment problem: special cases and relatives
, 1995
"... Financial support by the "Fonds zur F"orderung der wissenschaftlichen Forschung, Projekt P8971PHY", by the "Christian Doppler Laboratorium f"ur Diskrete Optimierung " and by the "Spezialforschungsbereich, Projektbereich Diskrete Optimierung " is gratefully ac ..."
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Cited by 1 (0 self)
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Financial support by the "Fonds zur F"orderung der wissenschaftlichen Forschung, Projekt P8971PHY", by the "Christian Doppler Laboratorium f"ur Diskrete Optimierung " and by the "Spezialforschungsbereich, Projektbereich Diskrete Optimierung " is gratefully acknowledged. Prind"erve t"e mi Acknowledgments First of all, I express my deepest gratitude to my supervisor Prof. Rainer E. Burkard for his manifold help and encouragement during the last three years. He motivated me to investigate the quadratic assignment problem (QAP) and its generalizations. I appreciate very much the opportunity to benefit from his long and rich experience with the QAP. Prof. Burkard's support was decisive for providing the financial basis which enabled my graduate studies. Next, I would like to thank Franz Rendl for his willingness to be the second referee of this thesis.
Selected Topics on Assignment Problems
, 1999
"... . We survey recent developments in the fields of bipartite matchings, linear sum assignment and bottleneck assignment problems and applications, multidimensional assignment problems, quadratic assignment problems, in particular lower bounds, special cases and asymptotic results, biquadratic and ..."
Abstract

Cited by 1 (0 self)
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. We survey recent developments in the fields of bipartite matchings, linear sum assignment and bottleneck assignment problems and applications, multidimensional assignment problems, quadratic assignment problems, in particular lower bounds, special cases and asymptotic results, biquadratic and communication assignment problems. Keywords: Assignment problem, bottleneck assignment problem, multidimensional assignment problem, quadratic assignment problem, special cases, asymptotic theory, quadratic bottleneck assignment problem, biquadratic assignment problem, communication assignment problem. AMSclassification: 90C27, 90B80, 68Q25, 90C05 1 Introduction Assignment problems deal with the question how to assign n items (jobs, students) to n other items (machines, tasks). Their underlying combinatorial structure is an assignment, which is nothing else than a bijective mapping ' between two finite sets of n elements. In the optimization problem we are looking for the best assign...
An Asymptotical Study of Combinatorial Optimization by Means of Statistical Mechanics
, 2003
"... The analogy between combinatorial optimization and statistical mechanics has proven to be a fruitful object of study. Simulated annealing, a metaheuristic for combinatorial optimization problems, is based on this analogy. In this paper ..."
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The analogy between combinatorial optimization and statistical mechanics has proven to be a fruitful object of study. Simulated annealing, a metaheuristic for combinatorial optimization problems, is based on this analogy. In this paper
The Quadratic Assignment Problem ∗
"... 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, an ..."
Abstract
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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 related to the QAP, e.g. the biquadratic assignment problem, and discusses the relationship between the QAP and other well known combinatorial optimization problems, e.g. the traveling salesman problem, the graph partitioning problem, etc. The paper will appear in the Handbook of Combinatorial Optimization to be published