Algorithms on Trees and Graphs

By: Gabriel Valiente

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Hardcover | 5 September 2002

At a Glance

Hardcover
508 Pages

Dimensions(cm)
24.13 x 15.88 x 3.18

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Published: 12th October 2021

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Graph algorithms is a well-established subject in mathematics and computer science. Beyond classical application fields, like approximation, combinatorial optimization, graphics, and operations research, graph algorithms have recently attracted increased attention from computational molecular biology and computational chemistry. Centered around the fundamental issue of graph isomorphism, this text goes beyond classical graph problems of shortest paths, spanning trees, flows in networks, and matchings in bipartite graphs. Advanced algorithmic results and techniques of practical relevance are presented in a coherent and consolidated way. This book introduces graph algorithms on an intuitive basis followed by a detailed exposition in a literate programming style, with correctness proofs as well as worst-case analyses. Furthermore, full C++ implementations of all algorithms presented are given using the LEDA library of efficient data structures and algorithms. Numerous illustrations, examples, and exercises, and a comprehensive bibliography support students and professionals in using the book as a text and source of reference

Industry Reviews

From the reviews:

"The main theme of this (research) monograph on graph algorithms is the isomorphism problem (for trees and graphs). Algorithms are both described on an intuitive basis and presented (and discussed) in detail using Knuth's literate programming style (C++, using the LEDA library). Besides offering an introduction to an interesting and important subject (with applications, e.g., in biology and chemistry), it also is a valuable (and unified) reference to material previously only available in research papers." (P. Schmitt, Monatshefte fuer Mathematik, Vol. 142 (4), 2004)

"The book goes beyond classical graph problems and addresses algorithmic problems with practical applications. ... will have a great potential in the hands of a dedicated teacher who is both willing and capable of using the software. Because much of the material in the book was previously only available in specialized research literature, this book will be very valuable also for researchers of algorithmic graph theory. This richly illustrated book has an extensive bibliography and several appendices describing the software." (Matti Vuorinen, Zentralblatt MATH, Vol. 1007, 2003)

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You Can Find This Book In

Non-Fiction Mathematics Combinatorics & Graph Theory Algebra Computing & I.T.Computer Programming & Software Development Algorithms & Data Structures Computer Science Mathematical Theory of Computation Maths for Computer Scientists Graphical & Digital Media Applications 3D Graphics & Modelling

Science Biology, Life Sciences Databases Artificial Intelligence

Introduction
Introduction	p. 3
Trees and Graphs	p. 3
Literate Programming	p. 23
Implementation Correctness	p. 28
Representation of Trees and Graphs	p. 34
Summary	p. 49
Bibliographic Notes	p. 49
Review Problems	p. 50
Exercises	p. 51
Algorithmic Techniques	p. 55
The Tree Edit Distance Problem	p. 55
Backtracking	p. 70
Branch-and-Bound	p. 80
Divide-and-Conquer	p. 85
Dynamic Programming	p. 94
Summary	p. 107
Bibliographic Notes	p. 107
Review Problems	p. 108
Exercises	p. 110
Algorithms on Trees
Tree Traversal	p. 113
Preorder Traversal of a Tree	p. 113
Postorder Traversal of a Tree	p. 119
Top-Down Traversal of a Tree	p. 124
Bottom-Up Traversal of a Tree	p. 129
Applications	p. 135
Summary	p. 145
Bibliographic Notes	p. 145
Review Problems	p. 146
Exercises	p. 147
Tree Isomorphism	p. 151
Tree Isomorphism	p. 151
Subtree Isomorphism	p. 170
Maximum Common Subtree Isomorphism	p. 206
Applications	p. 239
Summary	p. 242
Bibliographic Notes	p. 244
Review Problems	p. 246
Exercises	p. 249
Algorithms on Graphs
Graph Traversal	p. 255
Depth-First Traversal of a Graph	p. 255
Breadth-First Traversal of a Graph	p. 276
Applications	p. 288
Summary	p. 294
Bibliographic Notes	p. 294
Review Problems	p. 295
Exercises	p. 297
Clique, Independent Set, and Vertex Cover	p. 299
Cliques, Maximal Cliques, and Maximum Cliques	p. 299
Maximal and Maximum Independent Sets	p. 322
Minimal and Minimum Vertex Covers	p. 332
Applications	p. 341
Summary	p. 346
Bibliographic Notes	p. 346
Review Problems	p. 347
Exercises	p. 348
Graph Isomorphism	p. 351
Graph Isomorphism	p. 351
Graph Automorphism	p. 363
Subgraph Isomorphism	p. 367
Maximal Common Subgraph Isomorphism	p. 377
Applications	p. 389
Summary	p. 392
Bibliographic Notes	p. 392
Review Problems	p. 394
Exercises	p. 395
Appendices
An Overview of LEDA	p. 401
Introduction	p. 401
Data Structures	p. 402
Fundamental Graph Algorithms	p. 424
A Simple Representation of Trees	p. 426
A Simple Implementation of Radix Sort	p. 434
Bibliographic Notes	p. 445
Interactive Demonstration of Graph Algorithms	p. 447
Program Modules	p. 453
Bibliography	p. 459
Index	p. 489
Table of Contents provided by Syndetics. All Rights Reserved.

Algorithms on Trees and Graphs

At a Glance

New Edition

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

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