Graphs, Networks and Algorithms | Date: 08 May 2011, 00:34
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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.
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 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." (Peter B. Gibbons, Auckland, Zentralblatt fur Mathematik 1061, 2005)
Contents
Preface to the Third Edition
Preface to the Second Edition
Preface to the First Edition
1 Basic Graph Theory
2 Algorithms and Complexity
3 Shortest Paths
4 Spanning Trees
5 The Greedy Algorithm
6 Flows
7 Combinatorial Applications
8 Connectivity and Depth First Search
9 Colorings
10 Circulations
11 The Network Simplex Algorithm
12 Synthesis of Networks
13 Matchings
14 Weighted matchings
15 A Hard Problem: The TSP
A Some NP-Complete Problems
B Solutions
B.1 Solutions for Chapter 1
B.2 Solutions for Chapter 2
B.3 Solutions for Chapter 3
B.4 Solutions for Chapter 4
B.5 Solutions for Chapter 5
B.6 Solutions for Chapter 6
B.7 Solutions for Chapter 7
B.8 Solutions for Chapter 8
B.9 Solutions for Chapter 9
B.10 Solutions for Chapter 10
B.11 Solutions for Chapter 11
B.12 Solutions for Chapter 12
B.13 Solutions for Chapter 13
B.14 Solutions for Chapter 14
B.15 Solutions for Chapter 15
C List of Symbols
C.1 General Symbols
C.2 Special Symbols
References
Index
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