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Combinatorial Optimization：Algorithms and Complexity

作者: Christos 著 , Kenneth Steiglitz 著

出版社: Oversea Publishing House

出版时间: 1998-01

版次: 1

ISBN: 9780486402581

定价: 187.50

装帧: 平装

开本: 其他

纸张: 胶版纸

页数: 528页

正文语种: 英语

丛书: Dover Books on Computer Science

分类: 外文古旧书>英文书>工程技术

Clearlywrittengraduate-leveltextconsiderstheSovietellipsoidalgorithmforlinearprogramming;efficientalgorithmsfornetworkflow,matching,spanningtrees,andmatroids;thetheoryofNP-completeproblems;approximationalgorithms,localsearchheuristicsforNP-completeproblems,more."Mathematicianswishingaself-containedintroductionneedlooknofurther." PREFACE TO THE DOVER EDITION PREFACE

Chapter 1 OPTIMIZATION PROBLEMS

　1.1 Introduction

　1.2 Optimization Problems

　1.3 Neighborhoods

　1.4 Local and Global Optima

　1.5 Convex Sets and Functions

　1.6 Convex Programming Problems

　Problems

　Notes and References

　Appendix: Terminology and Notation

　A.1 Linear Algebra

　A.2 Graph Theory

　A.3 Pidgin Algol

Chapter2 THE SIMPLEX ALGORITHM

　2.1  Forfns of the Linear Programming Problem

　2.2 Basic Feasible Solutions

　2.3 The Geometry of Linear Programs

　　2.3.1  Linear and Affine Spaces

　　2.3.2 Convex Polytopes

　　2.3.3 Polytopes and LP

　2.4 Moving from bfs to bfs

　2.5 Organization of a Tableau

　2.6 Choosing a Profitable Column

　2.7 Degeneracy and Bland's Anticycling Algorithm

　2.8 Beginning the Simplex Algorithm

　2.9 Geometric Aspects of Pivoting

　Problems

　Notes and References

Chapter 3 DUALITY

　3.1 The Dual of a Linear Program in General Form

　3.2 Complementary Slackness

　3.3 Farkas' Lemma

　3.4 The Shortest-Path Problem and Its Dual

　3.5 Dual Information in the Tableau

　3.6 The Dual Simplex Algorithm

　3.7 Interpretation of the Dual Simplex Algorithm

　Problems

　Notes and References

Chapter 4 COMPUTATIONAL CONSIDERATIONS FOR THE SIMPLEX ALGORITHM

　4.1 The Revised Simplex Algorithm

　4.2 Computational Implications of the Revised Simple Algorithm

　4.3 The Max-Flow Problem and Its Solution by the Revised Method

　4.4 Dantzig-Wolfe Decomposition

　Problems

　Notes and References

Chapter 5 THE PRIMAL-DUAL ALGORITHM

Chapter 6 PRIMAL-DUAL ALGORITHMS FOR MAX-FLOW AND SHORTEST PATH：FORD-FULKERSON AND DIJKSTRA

Chapter 7 PRIMAL-DUAL ALGORITHMS FOR MIN-COST FLOW

Chapter 8 ALGORIT MS AND COMPLEXITY

Chapter 9 EFFICIENT ALGORITHMS FOR THE  MAX-FLOW PROMBLEM

Chapter 10 ALGORITHMS FOR MATCHING

Chapter 11 WEIGHTED MATCHING

Chapter 12 SPANNING TREES AND MATROIDS

Chapter 13 INTEGER LINEAR PROGRAMMING

Chapter 14 A CUTTING-PLANE ALGORITHM FOR INTEGER LINEAR PROGRAMS

Chapter 15 NP-COM PLETE PROBLEMS

Chapter 16 MORE ABOUT NP-COMPLETENESS

Chapter 17 APPROXIMATION ALGORITHMS

Chapter 18 BRANCH-AND-BOUND AND DYNAMIC PROGRAMMING

Chapter 19 LOCAL SEARCH

INDEX
内容简介:
Clearlywrittengraduate-leveltextconsiderstheSovietellipsoidalgorithmforlinearprogramming;efficientalgorithmsfornetworkflow,matching,spanningtrees,andmatroids;thetheoryofNP-completeproblems;approximationalgorithms,localsearchheuristicsforNP-completeproblems,more."Mathematicianswishingaself-containedintroductionneedlooknofurther."
目录:
PREFACE TO THE DOVER EDITION PREFACE

Chapter 1 OPTIMIZATION PROBLEMS

　1.1 Introduction

　1.2 Optimization Problems

　1.3 Neighborhoods

　1.4 Local and Global Optima

　1.5 Convex Sets and Functions

　1.6 Convex Programming Problems

　Problems

　Notes and References

　Appendix: Terminology and Notation

　A.1 Linear Algebra

　A.2 Graph Theory

　A.3 Pidgin Algol

Chapter2 THE SIMPLEX ALGORITHM

　2.1  Forfns of the Linear Programming Problem

　2.2 Basic Feasible Solutions

　2.3 The Geometry of Linear Programs

　　2.3.1  Linear and Affine Spaces

　　2.3.2 Convex Polytopes

　　2.3.3 Polytopes and LP

　2.4 Moving from bfs to bfs

　2.5 Organization of a Tableau

　2.6 Choosing a Profitable Column

　2.7 Degeneracy and Bland's Anticycling Algorithm

　2.8 Beginning the Simplex Algorithm

　2.9 Geometric Aspects of Pivoting

　Problems

　Notes and References

Chapter 3 DUALITY

　3.1 The Dual of a Linear Program in General Form

　3.2 Complementary Slackness

　3.3 Farkas' Lemma

　3.4 The Shortest-Path Problem and Its Dual

　3.5 Dual Information in the Tableau

　3.6 The Dual Simplex Algorithm

　3.7 Interpretation of the Dual Simplex Algorithm

　Problems

　Notes and References

Chapter 4 COMPUTATIONAL CONSIDERATIONS FOR THE SIMPLEX ALGORITHM

　4.1 The Revised Simplex Algorithm

　4.2 Computational Implications of the Revised Simple Algorithm

　4.3 The Max-Flow Problem and Its Solution by the Revised Method

　4.4 Dantzig-Wolfe Decomposition

　Problems

　Notes and References

Chapter 5 THE PRIMAL-DUAL ALGORITHM

Chapter 6 PRIMAL-DUAL ALGORITHMS FOR MAX-FLOW AND SHORTEST PATH：FORD-FULKERSON AND DIJKSTRA

Chapter 7 PRIMAL-DUAL ALGORITHMS FOR MIN-COST FLOW

Chapter 8 ALGORIT MS AND COMPLEXITY

Chapter 9 EFFICIENT ALGORITHMS FOR THE  MAX-FLOW PROMBLEM

Chapter 10 ALGORITHMS FOR MATCHING

Chapter 11 WEIGHTED MATCHING

Chapter 12 SPANNING TREES AND MATROIDS

Chapter 13 INTEGER LINEAR PROGRAMMING

Chapter 14 A CUTTING-PLANE ALGORITHM FOR INTEGER LINEAR PROGRAMS

Chapter 15 NP-COM PLETE PROBLEMS

Chapter 16 MORE ABOUT NP-COMPLETENESS

Chapter 17 APPROXIMATION ALGORITHMS

Chapter 18 BRANCH-AND-BOUND AND DYNAMIC PROGRAMMING

Chapter 19 LOCAL SEARCH

INDEX

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Combinatorial Optimization：Algorithms and Complexity

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