Algorithmic Aspects of Graph Connectivity

by Hiroshi Nagamochi, Toshihide Ibaraki

Overview

Algorithmic Aspects of Graph Connectivity is the first comprehensive book on this central notion in graph and network theory, emphasizing its algorithmic aspects. Because of its wide applications in the fields of communication, transportation, and production, graph connectivity has made tremendous algorithmic progress under the influence of the theory of complexity and algorithms in modern computer science. The book contains various definitions of connectivity, including edge-connectivity and vertex-connectivity, and their ramifications, as well as related topics such as flows and cuts. The authors comprehensively discuss new concepts and algorithms that allow for quicker and more efficient computing, such as maximum adjacency ordering of vertices. Covering both basic definitions and advanced topics, this book can be used as a textbook in graduate courses in mathematical sciences, such as discrete mathematics, combinatorics, and operations research, and as a reference book for specialists in discrete mathematics and its applications.

Product Details

ISBN-13:	9781108735490
Publisher:	Cambridge University Press
Publication date:	05/16/2019
Series:	Encyclopedia of Mathematics and its Applications , #123
Pages:	391
Product dimensions:	6.14(w) x 9.21(h) x 0.79(d)

About the Author

Hiroshi Nagamochi is a professor at the Graduate School of Informatics, Kyoto University, Japan. He is a member of the Operations Research Society of Japan and the Information Processing Society.

Toshihide Ibaraki is a Professor with Kwansei Gakuin University, Japan and Professor Emeritus of Kyoto University, Japan. He is a Fellow of the ACM and Operations Research Society of Japan.

Table of Contents

1. Introduction; 2. MA ordering and forest decompositions; 3. Minimum cuts; 4. Cut enumeration; 5. Cactus representations; 6. Extreme vertex sets; 7. Edge-splitting; 8. Connectivity augmentation; 9. Source location problems; 10. Submodular and posi-modular set functions.

Editorial Reviews

"... A comprehensive graduate level text and a worth addition to a professional library."
Book News

"This fine graduate-level textbook discusses the algorithmic efficiency of graph connectivity problems. What is impressive about this book is the unified framework in which algorithmic efficiency is discussed."
Mukkai S. Krishnamoorthy, Mathematical Reviews

From the Publisher