Algorithmic Aspects of Graph Connectivity

The first really thorough book to discuss this central notion in graph and network theory, emphasizing its algorithmic aspects.

Hiroshi Nagamochi (Author), Toshihide Ibaraki (Author)

9781108735490, Cambridge University Press

Paperback / softback, published 16 May 2019

391 pages
23.4 x 15.6 x 2 cm, 0.8 kg

'… comprehensive and detailed …' EMS Newsletter

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 thoroughly 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.

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.

Subject Areas: Algorithms & data structures [UMB], Combinatorics & graph theory [PBV]