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Handbook of Graph Theory, Combinatorial Optimization, and Algorithms




ISBN 9781584885955
Published December 14, 2015 by Chapman and Hall/CRC
1244 Pages 345 B/W Illustrations

 
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Book Description

The fusion between graph theory and combinatorial optimization has led to theoretically profound and practically useful algorithms, yet there is no book that currently covers both areas together. Handbook of Graph Theory, Combinatorial Optimization, and Algorithms is the first to present a unified, comprehensive treatment of both graph theory and combinatorial optimization.

Divided into 11 cohesive sections, the handbook’s 44 chapters focus on graph theory, combinatorial optimization, and algorithmic issues. The book provides readers with the algorithmic and theoretical foundations to:

  • Understand phenomena as shaped by their graph structures
  • Develop needed algorithmic and optimization tools for the study of graph structures
  • Design and plan graph structures that lead to certain desirable behavior

With contributions from more than 40 worldwide experts, this handbook equips readers with the necessary techniques and tools to solve problems in a variety of applications. Readers gain exposure to the theoretical and algorithmic foundations of a wide range of topics in graph theory and combinatorial optimization, enabling them to identify (and hence solve) problems encountered in diverse disciplines, such as electrical, communication, computer, social, transportation, biological, and other networks.

Table of Contents

Basic Concepts and Algorithms
Basic Concepts in Graph Theory and Algorithms
Subramanian Arumugam and Krishnaiyan "KT" Thulasiraman
Basic Graph Algorithms
Krishnaiyan "KT" Thulasiraman
Depth-First Search and Applications
Krishnaiyan "KT" Thulasiraman

Flows in Networks
Maximum Flow Problem
F. Zeynep Sargut, Ravindra K. Ahuja, James B. Orlin, and Thomas L. Magnanti
Minimum Cost Flow Problem
Balachandran Vaidyanathan, Ravindra K. Ahuja, James B. Orlin, and Thomas L. Magnanti
Multi-Commodity Flows
Balachandran Vaidyanathan, Ravindra K. Ahuja, James B. Orlin, and Thomas L. Magnanti

Algebraic Graph Theory
Graphs and Vector Spaces
Krishnaiyan "KT" Thulasiraman and M.N.S. Swamy
Incidence, Cut, and Circuit Matrices of a Graph
Krishnaiyan "KT" Thulasiraman and M.N.S. Swamy
Adjacency Matrix and Signal Flow Graphs
Krishnaiyan "KT" Thulasiraman and M.N.S. Swamy
Adjacency Spectrum and the Laplacian Spectrum of a Graph
R. Balakrishnan
Resistance Networks, Random Walks, and Network Theorems
Krishnaiyan "KT" Thulasiraman and Mamta Yadav

Structural Graph Theory
Connectivity
Subramanian Arumugam and Karam Ebadi
Connectivity Algorithms
Krishnaiyan "KT" Thulasiraman
Graph Connectivity Augmentation
András Frank and Tibor Jordán
Matchings
Michael D. Plummer
Matching Algorithms
Krishnaiyan "KT" Thulasiraman
Stable Marriage Problem
Shuichi Miyazaki
Domination in Graphs
Subramanian Arumugam and M. Sundarakannan
Graph Colorings
Subramanian Arumugam and K. Raja Chandrasekar

Planar Graphs
Planarity and Duality
Krishnaiyan "KT" Thulasiraman and M.N.S. Swamy
Edge Addition Planarity Testing Algorithm
John M. Boyer
Planarity Testing Based on PC-Trees
Wen-Lian Hsu
Graph Drawing
Md. Saidur Rahman and Takao Nishizeki

Interconnection Networks
Introduction to Interconnection Networks
S.A. Choudum, Lavanya Sivakumar, and V. Sunitha
Cayley Graphs
S. Lakshmivarahan, Lavanya Sivakumar, and S.K. Dhall
Graph Embedding and Interconnection Networks
S.A. Choudum, Lavanya Sivakumar, and V. Sunitha

Special Graphs
Program Graphs
Krishnaiyan "KT" Thulasiraman
Perfect Graphs
Chính T. Hoàng and R. Sritharan
Tree-Structured Graphs
Andreas Brandstädt and Feodor F. Dragan

Partitioning
Graph and Hypergraph Partitioning
Sachin B. Patkar and H. Narayanan

Matroids
Matroids
H. Narayanan and Sachin B. Patkar
Hybrid Analysis and Combinatorial Optimization
H. Narayanan

Probabilistic Methods, Random Graph Models, and Randomized Algorithms
Probabilistic Arguments in Combinatorics
C.R. Subramanian
Random Models and Analyses for Chemical Graphs
Daniel Pascua, Tina M. Kouri, and Dinesh P. Mehta
Randomized Graph Algorithms: Techniques and Analysis
Surender Baswana and Sandeep Sen

Coping with NP-Completeness
General Techniques for Combinatorial Approximation
Sartaj Sahni
ε-Approximation Schemes for the Constrained Shortest Path Problem
Krishnaiyan "KT" Thulasiraman
Constrained Shortest Path Problem: Lagrangian Relaxation-Based Algorithmic Approaches
Ying Xiao and Krishnaiyan "KT" Thulasiraman
Algorithms for Finding Disjoint Paths with QoS Constraints
Alex Sprintson and Ariel Orda
Set-Cover Approximation
Neal E. Young
Approximation Schemes for Fractional Multicommodity Flow Problems
George Karakostas
Approximation Algorithms for Connectivity Problems
Ramakrishna Thurimella
Rectilinear Steiner Minimum Trees
Tao Huang and Evangeline F.Y. Young
Fixed-Parameter Algorithms and Complexity
Venkatesh Raman and Saket Saurabh

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Editor(s)

Biography

Editor-in-Chief
Krishnaiyan "KT" Thulasiraman
is a professor and Hitachi Chair in Computer Science at the University of Oklahoma and a professor emeritus in electrical and computer engineering at Concordia University in Montreal. He is a fellow of the IEEE, AAAS, and the European Academy of Sciences. Dr. Thulasiraman has received several honors, including the Distinguished Alumnus Award of the Indian Institute of Technology Madras, IEEE Circuits and Systems Society Charles Desoer Technical Achievement Award, and IEEE Circuits and Systems Society Golden Jubilee Medal. He is the coauthor of two graduate-level textbooks on graphs, electrical networks, and algorithms. His research interests include graph theory, combinatorial optimization, and related algorithmic issues with a specific focus on applications in electrical and computer engineering and network science.

Editors
Subramanian Arumugam is a senior professor and director of the National Centre for Advanced Research in Discrete Mathematics at Kalasalingam University. He is also a visiting professor at Liverpool Hope University and an adjunct professor at Ball State University. Dr. Arumugam is the founding editor-in-chief of AKCE International Journal of Graphs and Combinatorics and author of 32 books and 195 journal papers. His current research interests include graph theory and its applications.

Andreas Brandstädt retired as a professor in computer science from the University of Rostock after 20 years. Dr. Brandstädt has published extensively in various international journals and conference proceedings. He is also the author of a textbook and coauthor of a widely cited monograph. His research interests include stochastics, complexity theory, formal languages, graph algorithms, graph theory, combinatorial optimization, and related algorithmic issues with a specific focus on efficient algorithms based on graph structure and graph classes with tree structure.

Takao Nishizeki is a professor emeritus at Tohoku University. He is a fellow of the ACM, IEEE, IEICE of Japan, Information Processing Society of Japan, and Bangladesh Academy of Sciences. Dr. Nishizeki has received several honors, including the Science and Technology Prize of the Japanese Ministry of Education, IEICE Achievement Award, ICF Best Research Award, Funai Information Science Promotion Award, TELECOM Technology Award, and many awards for best paper. His research interests include algorithms for planar graphs, edge coloring, network flows, VLSI routing, graph drawing, and cryptology.

Reviews

"To sum up,this book gives a lucid, deep,and panoramic view of ofgraphtheory, both broadly conceived and concentrating on its algorithmic and combinatorial optimization aspects. It will be of immense use to anyone with an interest in the area, researcher, teacher, or student, as a reference work or as a resource for self-study. It is a weighty but attractive volume, rich in content and richly illustrated. I highly recommended it!"

Frederic Green, Department of Mathematics and Computer Science Clark University Worcester.