Algorithms in Java, Part 5 Graph Algorithms

by Sedgewick, Robert

• ISBN13: 9780201361216
• ISBN10: 0201361213
• Edition: 3rd
• Format: Paperback
• Copyright: 2003-07-15
• Publisher: Addison-Wesley Professional

Summary

Once again, Robert Sedgewick provides a current and comprehensive introduction to important algorithms. The focus this time is on graph algorithms, which are increasingly critical for a wide range of applications, such as network connectivity, circuit design, scheduling, transaction processing, and resource allocation. In this book, Sedgewick offers the same successful blend of theory and practice that has made his work popular with programmers for many years. Michael Schidlowsky and Sedgewick have developed concise new Java implementations that both express the methods in a natural and direct manner and also can be used in real applications.Algorithms in Java, Third Edition, Part 5: Graph Algorithms is the second book in Sedgewick's thoroughly revised and rewritten series. The first book, Parts 1-4, addresses fundamental algorithms, data structures, sorting, and searching. A forthcoming third book will focus on strings, geometry, and a range of advanced algorithms. Each book's expanded coverage features new algorithms and implementations, enhanced descriptions and diagrams, and a wealth of new exercises for polishing skills. The natural match between Java classes and abstract data type (ADT) implementations makes the code more broadly useful and relevant for the modern object-oriented programming environment.The Web site for this book ( www.cs.princeton.edu/~rs/ ) provides additional source code for programmers along with a variety of academic support materials for educators.Coverage includes: A complete overview of graph properties and types Diagraphs and DAGs Minimum spanning trees Shortest paths Network flows Diagrams, sample Java code, and detailed algorithm descriptions A landmark revision, Algorithms in Java, Third Edition, Part 5 provides a complete tool set for programmers to implement, debug, and use graph algorithms across a wide range of computer applications. 0201361213B06272003

Author Biography

Robert Sedgewick is a Professor of Computer Science at Princeton University. He is a director of Adobe Systems and has served on the research staffs at Xerox PARC, the Institute for Defense Analyses, and INRIA Michael Schidlowsky, a Princeton graduate, is an independent software consultant specializing in object-oriented programming. Most recently he was the CTO of Teaching That Works and the founder of xSense Corporation

Table of Contents

Graph Algorithms
Graph Properties and Types	p. 3
Glossary	p. 7
Graph ADT	p. 16
Adjacency-Matrix Representation	p. 25
Adjacency-Lists Representation	p. 31
Variations, Extensions, and Costs	p. 36
Graph Generators	p. 46
Simple, Euler, and Hamilton Paths	p. 57
Graph-Processing Problems	p. 70
Graph Search	p. 81
Exploring a Maze	p. 82
Depth-First Search	p. 87
Graph-Search ADT Methods	p. 91
Properties of DFS Forests	p. 97
DFS Algorithms	p. 105
Separability and Biconnectivity	p. 112
Breadth-First Search	p. 121
Generalized Graph Search	p. 131
Analysis of Graph Algorithms	p. 140
Digraphs and DAGs	p. 149
Glossary and Rules of the Game	p. 152
Anatomy of DFS in Digraphs	p. 160
Reachability and Transitive Closure	p. 169
Equivalence Relations and Partial Orders	p. 182
DAGs	p. 186
Topological Sorting	p. 191
Reachability in DAGs	p. 202
Strong Components in Digraphs	p. 205
Transitive Closure Revisited	p. 217
Perspective	p. 222
Minimum Spanning Trees	p. 227
Representations	p. 230
Underlying Principles of MST Algorithms	p. 240
Prim's Algorithm and Priority-First Search	p. 247
Kruskal's Algorithm	p. 258
Boruvka's Algorithm	p. 264
Comparisons and Improvements	p. 268
Euclidean MST	p. 274
Shortest Paths	p. 277
Underlying Principles	p. 285
Dijkstra's Algorithm	p. 293
All-Pairs Shortest Paths	p. 304
Shortest Paths in Acyclic Networks	p. 313
Euclidean Networks	p. 322
Reduction	p. 328
Negative Weights	p. 345
Perspective	p. 363
Network Flow	p. 367
Flow Networks	p. 373
Augmenting-Path Maxflow Algorithms	p. 382
Preflow-Push Maxflow Algorithms	p. 410
Maxflow Reductions	p. 425
Mincost Flows	p. 443
Network Simplex Algorithm	p. 453
Mincost-Flow Reductions	p. 472
Perspective	p. 482
References for Part Five	p. 487
Index	p. 489
Table of Contents provided by Ingram. All Rights Reserved.

Excerpts

Graphs and graph algorithms are pervasive in modern computing applications. This book describes the most important known methods for solving the graph-processing problems that arise in practice. Its primary aim is to make these methods and the basic principles behind them accessible to the growing number of people in need of knowing them. The material is developed from first principles, starting with basic information and working through classical methods up through modern techniques that are still under development. Carefully chosen examples, detailed figures, and complete implementations supplement thorough descriptions of algorithms and applications. Algorithms This book is the second of three volumes that are intended to survey the most important computer algorithms in use today. The first volume (Parts 1-4) covers fundamental concepts (Part 1), data structures (Part 2), sorting algorithms (Part 3), and searching algorithms (Part 4); this volume (Part 5) covers graphs and graph algorithms; and the (yet to be published) third volume (Parts 6-8) covers strings (Part 6), computational geometry (Part 7), and advanced algorithms and applications (Part 8). The books are useful as texts early in the computer science curriculum, after students have acquired basic programming skills and familiarity with computer systems, but before they have taken specialized courses in advanced areas of computer science or computer applications. The books also are useful for self-study or as a reference for people engaged in the development of computer systems or applications programs because they contain implementations of useful algorithms and detailed information on these algorithms' performance characteristics. The broad perspective taken makes the series an appropriate introduction to the field. Together the three volumes comprise theThird Editionof a book that has been widely used by students and programmers around the world for many years. I have completely rewritten the text for this edition, and I have added thousands of new exercises, hundreds of new figures, dozens of new programs, and detailed commentary on all the figures and programs. This new material provides both coverage of new topics and fuller explanations of many of the classic algorithms. A new emphasis on abstract data types throughout the books makes the programs more broadly useful and relevant in modern object-oriented programming environments. People who have read previous editions will find a wealth of new information throughout; all readers will find a wealth of pedagogical material that provides effective access to essential concepts. These books are not just for programmers and computer-science students. Nearly everyone who uses a computer wants it to run faster or to solve larger problems. The algorithms that we consider represent a body of knowledge developed during the last 50 years that has become indispensable in the efficient use of the computer for a broad variety of applications. From N-body simulation problems in physics to genetic-sequencing problems in molecular biology, the basic methods described here have become essential in scientific research; and from database systems to Internet search engines, they have become essential parts of modern software systems. As the scope of computer applications becomes more widespread, so grows the impact of basic algorithms, particularly the fundamental graph algorithms covered in this volume. The goal of this book is to serve as a resource so that students and professionals can know and make intelligent use of graph algorithms as the need arises in whatever computer application they might undertake. Scope This book,Algorithms in C, Third Edition, Part 5: Graph Algorithms,contains six chapters that cover graph properties and types, graph search, directed graphs, minimal spanning