Topic
Assignment problem
About: Assignment problem is a research topic. Over the lifetime, 7588 publications have been published within this topic receiving 172820 citations. The topic is also known as: marriage problem.
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TL;DR: This chapter sees how the simplex method simplifies when it is applied to a class of optimization problems that are known as “network flow models” and finds an optimal solution that is integer-valued.
Abstract: In this chapter, you will see how the simplex method simplifies when it is applied to a class of optimization problems that are known as “network flow models.” You will also see that if a network flow model has “integer-valued data,” the simplex method finds an optimal solution that is integer-valued.
828 citations
TL;DR: A collection of electronically available data instances for the Quadratic Assignment Problem are described, indicating whether or not the problem is solved to optimality and the best known bounds for the problem are supplied.
Abstract: A collection of electronically available data instances for the Quadratic Assignment Problem is described. For each instance, we provide detailed information, indicating whether or not the problem is solved to optimality. If not, we supply the best known bounds for the problem. Moreover we survey available software and describe recent dissertations related to the Quadratic Assignment Problem.
826 citations
01 Apr 1990
TL;DR: This work applies the general approach to data structures, bin packing, graph coloring, and graph coloring to bipartite matching and shows that a simple randomized on-line algorithm achieves the best possible performance.
Abstract: There has been a great deal of interest recently in the relative power of on-line and off-line algorithms. An on-line algorithm receives a sequence of requests and must respond to each request as soon as it is receiveD. An off-line algorithm may wait until all requests have been received before determining its responses. One approach to evaluating an on-line algorithm is to compare its performance with that of the best possible off-line algorithm for the same problem. Thus, given a measure of "profit", the performance of an on-line algorithm can be measured by the worst-case ratio of its profit to that of the optimal off-line algorithm. This general approach has been applied in a number of contexts, including data structures [SITa], bin packing [CoGaJo], graph coloring [GyLe] and the k-server problem [MaMcSI]. Here we apply it to bipartite matching and show that a simple randomized on-line algorithm achieves the best possible performance.
807 citations
TL;DR: In this article, the authors present a solution technique for large scale road network equilibrium assignment and related flow problems with nonlinear costs, without explicitly considering any of the constraints, and without storing all of the individual decision variables.
766 citations
Book•
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01 Jan 2008
TL;DR: A comprehensive treatment of assignment problems from their conceptual beginnings in the 1920s through present-day theoretical, algorithmic, and practical developments can be found in this article, where 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.
Abstract: 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 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. Audience: Assignment Problems is a useful tool for researchers, practitioners, and graduate students. Researchers will benefit from the 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. Contents: Preface; Chapter 1: Introduction; Chapter 2: Theoretical Foundations; Chapter 3: Bipartite Matching Algorithms; Chapter 4: Linear Sum Assignment Problem; Chapter 5: Further Results on the Linear Sum Assignment Problem; Chapter 6: Other Types of Linear Assignment Problems; Chapter 7: Quadratic Assignment Problems: Formulations and Bounds; Chapter 8: Quadratic Assignment Problems: Algorithms; Chapter 9: Other Types of Quadratic Assignment Problems; Chapter 10: Multi-index Assignment Problems; Bibliography; Author Index; Subject Index
760 citations