Combinatorial Optimization 2st editon by William Cook ISBN 047155894X 9780471558941

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ISBN 10: 047155894X 
ISBN 13: 9780471558941
Author: William J. Cook; William H. Cunningham; William R. Pulleyblank; Alexander Schrijver

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.

Combinatorial Optimization 2st Table of contents:

1 Problems and Algorithms

1.1 Two Problems

1.2 Measuring Running Times

2 Optimal Trees and Paths

2.1 Minimum Spanning Trees

2.2 Shortest Paths

3 Maximum Flow Problems

3.1 Network Flow Problems

3.2 Maximum Flow Problems

3.3 Applications of Maximum Flow and Minimum Cut

3.4 Push-Relabel Maximum Flow Algorithms

3.5 Minimum Cuts in Undirected Graphs

3.5.1 Global Minimum Cuts

3.5.2 Cut-Trees

3.6 Multicommodity Flows

4 Minimum-Cost Flow Problems

4.1 Minimum-Cost Flow Problems

4.2 Primal Minimum-Cost Flow Algorithms

4.3 Dual Minimum-Cost Flow Algorithms

4.4 Dual Scaling Algorithms

5 Optimal Matchings

5.1 Matchings and Alternating Paths

5.2 Maximum Matching

5.3 Minimum-Weight Perfect Matchings

5.4 T-Joins and Postman Problems

5.5 General Matching Problems

5.6 Geometric Duality and the Goemans-Williamson Algorithm

6 Integrality of Polyhedra

6.1 Convex hulls

6.2 Polytopes

6.3 Facets

6.4 Integral Polytopes

6.5 Total Unimodularity

6.6 Total Dual Integrality

6.7 Cutting Planes

6.8 Separation and Optimization

7 The Traveling Salesman Problem

7.1 Introduction

7.2 Heuristics for the TSP

7.3 Lower Bounds

7.4 Cutting Planes

7.5 Branch and Bound

8 Matroids

8.1 Matroids and the Greedy Algorithm

8.2 Matroids: Properties, Axioms, Constructions

8.3 Matroid Intersection

8.4 Applications of Matroid Intersection

8.5 Weighted Matroid Intersection

9 NP and NP-Completeness

9.1 Introduction

9.2 Words

9.3 Problems

9.4 Algorithms and Running Time

9.5 The Class NP

9.6 NP-Completeness

9.7 NP-Completeness of the Satisfiability Problem

9.8 NP-Completeness of Some Other Problems

9.9 Turing Machines

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