Graphs, Networks and Algorithms

by Dieter Jungnickel

Overview

From the reviews of the 2nd edition

The substantial development effort of this text clearly shows through in this new edition with its clear writing, good organisation, comprehensive coverage of essential theory, and well-chosen applications. The proofs of important results and the representation of key algorithms in a Pascal-like notation allow this book to be used in a high-level undergraduate or low-level graduate course on graph theory, combinatorial optimization or computer science algorithms. The well-worked solutions to exercises are a real bonus for self study by students. The book is highly recommended.

Zentralblatt für Mathematik 2005

The third edition of this standard textbook contains additional material: two new application sections (on graphical codes and their decoding) and about two dozen further exercises (with solutions, as throughout the text). Moreover, recent developments have been discussed and referenced, in particular for the travelling salesman problem. The presentation has been improved in many places (for instance, in the chapters on shortest paths and on colorings), and a number of proofs have been reorganized, making them more precise or more transparent.

Product Details

ISBN-13:	9783642091865
Publisher:	Springer Berlin Heidelberg
Publication date:	11/30/2010
Series:	Algorithms and Computation in Mathematics , #5
Edition description:	Third Edition 2008
Pages:	650
Product dimensions:	6.10(w) x 9.25(h) x 0.36(d)

About the Author

Dieter Jungnickel is an internationally known mathematician working in the field of applied algebra, coding theory, design theory, finite geometry, codes and designs and combinatorial optimization.

He has published several well-known books, including “Optimization Methods”, “Finite Fields”, “Coding Theory” and “Graphs, Networks and Algorithms”, some of which have been published both in English and German.

Table of Contents

Prefaces.- Basic Graph Theory.- Algorithms and Complexity.- Shortest Paths.- Spanning Trees.- The Greedy Algorithm.- Flows.- Combinatorial Applications.- Connectivity and Depth First Search.- Colorings.- Circulations.- The Network Simplex Algorithm.- Synthesis of Networks.- Matchings.- Weighted Matchings.- A Hard Problem: The TSP.- Appendix A: Some NP-Complete Problems.- Appendix B: Solutions.- Appendix C: List of Symbols.- References.- Index.

Editorial Reviews

From reviews:

“.... The book is a first class textbook and seems to be indispensable for everybody who has to teach combinatorial optimization. It is very helpful for students, teachers, and researchers in this area. The author finds a striking synthesis of nice and interesting mathematical results and practical applications. ... the author pays much attention to the inclusion of well-chosen exercises. The reader does not remain helpless; solutions or at least hints are given in the appendix. Except for some small basic mathematical and algorithmic knowledge the book is self-contained.” (K. Engel, Mathematical Reviews (2002)

“This book has been a pleasure to read and review. Its title is brief and self-explanatory, and the book has been well-produced and designed for both reference and systematic use. .... Firstly, it is an extremely clear text; ... Secondly, the author is not ashamed to introduce practice and illustrations, so that this is not a “dry-as-dust” text in esoteric mathematics. Algorithms are presented in pseudocode, and their workings are thoroughly discussed. It is a comprehensive book. ... Therefore, if you have the slightest interest in the algorithms for graphs and networks, or in the theory of such models, then Jungnickel has produced a book that you ought to have available for reference.” (David K. Smith, University of Exeter, Journal of the Operational Research Society, 50 (1999)

“The substantial development effort of this text, involving multiple editions and trailing in the context of various workshops, university courses and seminar series, clearly shows through in this new edition with its clear writing, good organisation, comprehensive coverage of essential theory, and well-chosen applications. The proofs of important results and the representation of key algorithms in a Pascal-like notation allow this book to be used in a high-level undergraduate or low-level graduate course on graphtheory, combinatorial optimization or computer science algorithms. The well-worked solutions to exercises are a real bonus for self study by students. The book is highly recommended.” (Peter B. Gibbons, Auckland, Zentralblatt für Mathematik 1061, 2005)

From the reviews of the second edition:

"This book … beginning from the very basic definitions of graph theory, quickly building a catalog of theorems, and ending with a complex suite of algorithms on graphs and networks. … At the end is a collection of NP-complete problems and an extensive bibliography. This text is suitable for graduate courses in combinatorics and graph theory, as well as for independent study and research by students, mathematicians, and professionals. It is a welcome addition to the library of choices of textbooks for these subjects." (William Fahle, SIGACT News, Vol. 36 (4), 2005)

From the reviews of the third edition:

"The third edition of this standard textbook contains further new material on graphical codes and their decoding, and many additional exercises. … The focus on algorithmic issues motivates challenging questions, and connects the presentation to many real applications. … appropriate for computer science and engineering students, in addition to students of mathematics. The diversity of applications represented is a real strength of the text. … provides connections to other areas of mathematics, and applications, that serve to motivate students. The book is highly recommended." (Charles J. Colbourn, Zentralblatt MATH, Vol. 1126 (3), 2008)

“The book treats the most important algorithmic problems concerning graphs and networks which are polynomially solvable. … The book is well written, clear and understandable and can also be recommended as text book for students and beginners in this field. There are many exercises (with solutions) and examples. It is an indispensable reference for anyone working with algorithmsand networks. The list of references is extensive.” (B. Krön, Monatshefte für Mathematik, Vol. 154 (4), August, 2008)

From the Publisher