Combinatorial Optimization

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John Wiley & Sons, Sep 30, 2011 - Mathematics - 368 pages
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A complete, highly accessible introduction to one of today's most exciting areas of applied mathematics

One of the youngest, most vital areas of applied mathematics, combinatorial optimization integrates techniques from combinatorics, linear programming, and the theory of algorithms. Because of its success in solving difficult problems in areas from telecommunications to VLSI, from product distribution to airline crew scheduling, the field has seen a ground swell of activity over the past decade.

Combinatorial Optimization is an ideal introduction to this mathematical discipline for advanced undergraduates and graduate students of discrete mathematics, computer science, and operations research. Written by a team of recognized experts, the text offers a thorough, highly accessible treatment of both classical concepts and recent results. The topics include:
* Network flow problems
* Optimal matching
* Integrality of polyhedra
* Matroids
* NP-completeness

Featuring logical and consistent exposition, clear explanations of basic and advanced concepts, many real-world examples, and helpful, skill-building exercises, Combinatorial Optimization is certain to become the standard text in the field for many years to come.
 

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Contents

1 Problems and Algorithms
1
2 Optimal Trees and Paths
9
3 Maximum Flow Problems
37
4 MinimumCost Flow Problems
91
5 Optimal Matchings
127
6 Integrality of Polyhedra
199
7 The Traveling Salesman Problem
241
8 Matroids
273
9 NP and NPCompleteness
309
APPENDIX A Linear Programming
325
Bibliography
337
Index
347
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About the author (2011)

WILLIAM J. COOK is a professor in the Department of Computational and Applied Mathematics at Rice University. WILLIAM H. CUNNINGHAM is a professor in the Department of Combinatorics and Optimization at the University of Waterloo. WILLIAM R. PULLEYBLANK is Director of Mathematical Sciences at IBM Watson Research in Yorktown Heights, New York. ALEXANDER SCHRIJVER is a department head at the Centrum voor Wiskunde en Informatica, with a joint appointment as a professor at the University of Amsterdam.

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