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Combinatorial Algorithms Enlarged Second Edition book cover, ISBN 9780486419626

Combinatorial Algorithms Enlarged Second Edition

by Hu, T. C.; Shing, M. T.

ISBN13: 9780486419626
ISBN10: 0486419622
eBook ISBN(s): 9780486152943
Edition: 2nd
Format: Paperback
Copyright: 2002-04-15
Publisher: Dover Publications

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Summary

Updated second edition presents algorithms for shortest paths, maximum flows, dynamic programming and backtracking. Also discussed are binary trees, heuristic and near optimums, matrix multiplication, and NP-complete problems. New to this edition: how to mix known algorithms and create new ones. Features 153 black-and-white illustrations and 23 tables. Exercises, with answers at the ends of chapters.

Table of Contents

Shortest Paths

Graph Terminology

1

(2)

Shortest Path

3

(7)

Multiterminal Shortest Paths

10

(7)

Decomposition Algorithm

17

(6)

Acyclic Network

23

(1)

Shortest Paths in a General Network

24

(3)

Minimum Spanning Tree

27

(3)

Breadth-first-search and Depth-first-search

30

(10)

Maximum Flows

Maximum Flow

40

(6)

Algorithms for Max Flows

46

(14)

Ford and Fulkerson

46

(7)

Karzanov's Algorithm

53

(3)

MPM Algorihtms

56

(2)

Analysis of Algorithms

58

(2)

Multi-terminal Maximum Flows

60

(23)

Realization

62

(1)

Analysis

63

(13)

Synthesis

76

(6)

Multi-commodity Flows

82

(1)

Minimum Cost Flows

83

(3)

Applications

86

(21)

Sets of Distinct Representatives

87

(2)

PERT

89

(5)

Optimum Communication Spanning Tree

94

(13)

Dynamic Programming

Introduction

107

(6)

Knapsack Problem

113

(8)

Two-dimensional Knapsack Problem

121

(6)

Minimum-Cost Alphabetic Tree

127

(5)

Summary

132

(6)

Backtracking

Introduction

138

(7)

Estimating the Efficiency of Backtracking

145

(2)

Branch and Bound

147

(4)

Game-tree

151

(11)

Binary Tree

Introduction

162

(2)

Huffman's Tree

164

(7)

Alphabetic Tree

171

(2)

Hu-Tucker Algorithm

173

(7)

Feasibility and Optimality

180

(8)

Garsia and Wachs' Algorithm

188

(3)

Regular Cost Function

191

(4)

T-ary Tree and Other Results

195

(7)

Heuristic and Near Optimum

Greedy Algorithm

202

(7)

Bin-packing

209

(13)

Job-scheduling

222

(7)

Job-scheduling (tree-constraints)

229

(11)

Matrix Multiplication

Strassen's Matrix Multiplication

240

(1)

Optimum Order of Multiplying Matrices

241

(1)

Partitioning a Convex Polygon

242

(12)

The Heuristic Algorithm

254

(19)

NP-complete

Introduction

273

(2)

Polynomial Algorithms

275

(3)

Nondeterministic Algorithms

278

(1)

NP-complete Problems

279

(3)

Facing a New Problem

282

(6)

Local Indexing Algorithms

Mergers of Algorithms

288

(3)

Maximum Flows and Minimum Cuts

291

(2)

Maximum Adjacency and Minimum Separation

293

(7)

Gomory-Hu Tree

Tree Edges and Tree Links

300

(4)

Contraction

304

(1)

Domination

305

(3)

Equivalent Formulations

308

(6)

Optimum Mergers of Companies

308

(1)

Optimum Circle Partition

309

(5)

Extreme Stars and Host-feasible Circles

314

(6)

The High-level Approach

320

(6)

Chop-stick Method

326

(3)

Relationship Between Phases

329

(2)

The Staircase Diagram

331

(6)

Complexity Issues

337

(3)

Appendix A. Comments on Chapters 2, 5 & 6

Ancestor Trees

340

(1)

Minimum Surface or Plateau Problem

341

(1)

Comments on Binary Trees in Chapter 5

342

(4)

A Simple Proof of the Hu-Tucker Algorithm

343

(1)

Binary Search Trees

344

(1)

Binary Search on a Tape

345

(1)

Comments on §6.2, Bin-packing

346

Appendix B. Network Algebra

Supplemental Materials

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