Assignment Problems is a useful tool for researchers, practitioners and graduate students. In 10 self-contained chapters, it provides a comprehensive treatment of assignment problems from their conceptual beginnings through present-day theoretical, algorithmic and practical developments. The topics covered include bipartite matching algorithms, linear assignment problems, quadratic assignment problems, multi-index assignment problems and many variations of these. Researchers will benefit from the detailed exposition of theory and algorithms related to assignment problems, including the basic linear sum assignment problem and its variations. Practitioners will learn about practical applications of the methods, the performance of exact and heuristic algorithms, and software options. This book also can serve as a text for advanced courses in areas related to discrete mathematics and combinatorial optimisation. The revised reprint provides details on a recent discovery related to one of Jacobi's results, new material on inverse assignment problems and quadratic assignment problems, and an updated bibliography.

This book provides a comprehensive treatment of assignment problems from their conceptual beginnings in the 1920s through present-day theoretical, algorithmic, and practical developments. The revised reprint provides details on a recent discovery related to one of Jacobi's results, new material on inverse assignment problems and quadratic assignment problems, and an updated bibliography. The authors have organized the book into 10 self-contained chapters to make it easy for readers to use the specific chapters of interest to them without having to read the book linearly. The topics covered include bipartite matching algorithms, linear assignment problems, quadratic assignment problems, multi-index assignment problems, and many variations of these problems. Exercises in the form of numerical examples provide readers with a method of self-study or students with homework problems, and an associated webpage offers applets that readers can use to execute some of the basic algorithms as well as links to computer codes that are available online. Researchers will benefit from the book's detailed exposition of theory and algorithms related to assignment problems, including the basic linear sum assignment problem and its many variations. Practitioners will learn about practical applications of the methods, the performance of exact and heuristic algorithms, and software options. This book also can serve as a text for advanced courses in discrete mathematics, integer programming, combinatorial optimization, and algorithmic computer science.

Nonlinear Assignment Problems (NAPs) are natural extensions of the classic Linear Assignment Problem, and despite the efforts of many researchers over the past three decades, they still remain some of the hardest combinatorial optimization problems to solve exactly. The purpose of this book is to provide in a single volume, major algorithmic aspects and applications of NAPs as contributed by leading international experts. The chapters included in this book are concerned with major applications and the latest algorithmic solution approaches for NAPs. Approximation algorithms, polyhedral methods, semidefinite programming approaches and heuristic procedures for NAPs are included, while applications of this problem class in the areas of multiple-target tracking in the context of military surveillance systems, of experimental high energy physics, and of parallel processing are presented. Audience: Researchers and graduate students in the areas of combinatorial optimization, mathematical programming, operations research, physics, and computer science.

The quadratic assignment problem (QAP) was introduced in 1957 by Koopmans and Beckmann to model a plant location problem. Since then the QAP has been object of numerous investigations by mathematicians, computers scientists, ope- tions researchers and practitioners. Nowadays the QAP is widely considered as a classical combinatorial optimization problem which is (still) attractive from many points of view. In our opinion there are at last three main reasons which make the QAP a popular problem in combinatorial optimization. First, the number of re- life problems which are mathematically modeled by QAPs has been continuously increasing and the variety of the fields they belong to is astonishing. To recall just a restricted number among the applications of the QAP let us mention placement problems, scheduling, manufacturing, VLSI design, statistical data analysis, and parallel and distributed computing. Secondly, a number of other well known c- binatorial optimization problems can be formulated as QAPs. Typical examples are the traveling salesman problem and a large number of optimization problems in graphs such as the maximum clique problem, the graph partitioning problem and the minimum feedback arc set problem. Finally, from a computational point of view the QAP is a very difficult problem. The QAP is not only NP-hard and - hard to approximate, but it is also practically intractable: it is generally considered as impossible to solve (to optimality) QAP instances of size larger than 20 within reasonable time limits.

This book has been written for practitioners, researchers and stu dents in the fields of parallel and distributed computing. Its objective is to provide detailed coverage of the applications of graph theoretic tech niques to the problems of matching resources and requirements in multi ple computer systems. There has been considerable research in this area over the last decade and intense work continues even as this is being written. For the practitioner, this book serves as a rich source of solution techniques for problems that are routinely encountered in the real world. Algorithms are presented in sufficient detail to permit easy implementa tion; background material and fundamental concepts are covered in full. The researcher will find a clear exposition of graph theoretic tech niques applied to parallel and distributed computing. Research results are covered and many hitherto unpublished spanning the last decade results by the author are included. There are many unsolved problems in this field-it is hoped that this book will stimulate further research.

This book has been written for practitioners, researchers and stu dents in the fields of parallel and distributed computing. Its objective is to provide detailed coverage of the applications of graph theoretic tech niques to the problems of matching resources and requirements in multi ple computer systems. There has been considerable research in this area over the last decade and intense work continues even as this is being written. For the practitioner, this book serves as a rich source of solution techniques for problems that are routinely encountered in the real world. Algorithms are presented in sufficient detail to permit easy implementa tion; background material and fundamental concepts are covered in full. The researcher will find a clear exposition of graph theoretic tech niques applied to parallel and distributed computing. Research results are covered and many hitherto unpublished spanning the last decade results by the author are included. There are many unsolved problems in this field-it is hoped that this book will stimulate further research.