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E-raamat: Handbook of Graph Theory, Combinatorial Optimization, and Algorithms [Taylor & Francis e-raamat]

Edited by (University of Rostock, Germany), Edited by (Kalasalingam University, Krishnankoil, India), Edited by (Tohoku University, Sendai, Japan), Edited by (University of Oklahoma, Norman, USA)
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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 handbooks 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.
Preface xi
Editors xiii
Contributors xv
Section I Basic Concepts and Algorithms
Chapter 1 Basic Concepts in Graph Theory and Algorithms
3(18)
Subramanian Arumugam
Krishnaiyan "KT" Thulasiraman
Chapter 2 Basic Graph Algorithms
21(38)
Krishnaiyan "KT" Thulasiraman
Chapter 3 Depth-First Search and Applications
59(20)
Krishnaiyan "KT" Thulasiraman
Section II Flows in Networks
Chapter 4 Maximum Flow Problem
79(34)
F. Zeynep Sargut
Ravindra K. Ahuja
James B. Orlin
Thomas L. Magnanti
Chapter 5 Minimum Cost Flow Problem
113(44)
Balachandran Vaidyanathan
Ravindra K. Ahuja
James B. Orlin
Thomas L. Magnanti
Chapter 6 Multicommodity Flows
157(20)
Balachandran Vaidyanathan
Ravindra K. Ahuja
James B. Orlin
Thomas L. Magnanti
Section III Algebraic Graph Theory
Chapter 7 Graphs and Vector Spaces
177(14)
Krishnaiyan "KT" Thulasiraman
M. N. S. Swamy
Chapter 8 Incidence, Cut, and Circuit Matrices of a Graph
191(24)
Krishnaiyan "KT" Thulasiraman
M. N. S. Swamy
Chapter 9 Adjacency Matrix and Signal Flow Graphs
215(12)
Krishnaiyan "KT" Thulasiraman
M. N. S. Swamy
Chapter 10 Adjacency Spectrum and the Laplacian Spectrum of a Graph
227(20)
R. Balakrishnan
Chapter 11 Resistance Networks, Random Walks, and Network Theorems
247(26)
Krishnaiyan "KT" Thulasiraman
Mamta Yadav
Section IV Structural Graph Theory
Chapter 12 Connectivity
273(18)
Subramanian Arumugam
Karam Ebadi
Chapter 13 Connectivity Algorithms
291(24)
Krishnaiyan "KT" Thulasiraman
Chapter 14 Graph Connectivity Augmentation
315(34)
Andras Frank
Tibor Jordan
Chapter 15 Matchings
349(24)
Michael D. Plummer
Chapter 16 Matching Algorithms
373(30)
Krishnaiyan "KT" Thulasiraman
Chapter 17 Stable Marriage Problem
403(16)
Shuichi Miyazaki
Chapter 18 Domination in Graphs
419(30)
Subramanian Arumugam
M. Sundarakannan
Chapter 19 Graph Colorings
449(26)
Subramanian Arumugam
K. Raja Chandrasekar
Section V Planar Graphs
Chapter 20 Planarity and Duality
475(14)
Krishnaiyan "KT" Thulasiraman
M. N. S. Swamy
Chapter 21 Edge Addition Planarity Testing Algorithm
489(36)
John M. Boyer
Chapter 22 Planarity Testing Based on PC-Trees
525(12)
Wen-Lian Hsu
Chapter 23 Graph Drawing
537(50)
Md. Saidur Rahman
Takao Nishizeki
Section VI Interconnection Networks
Chapter 24 Introduction to Interconnection Networks
587(40)
S. A. Choudum
Lavanya Sivakumar
V. Sunitha
Chapter 25 Cayley Graphs
627(26)
S. Lakshmivarahan
Lavanya Sivakumar
S. K. Dhall
Chapter 26 Graph Embedding and Interconnection Networks
653(38)
S.A. Choudum
Lavanya Sivakumar
V. Sunitha
Section VII Special Graphs
Chapter 27 Program Graphs
691(16)
Krishnaiyan "KT" Thulasiraman
Chapter 28 Perfect Graphs
707(44)
Chinh T. Hoang
R. Sritharan
Chapter 29 Tree-Structured Graphs
751(78)
Andreas Brandstadt
Feodor F. Dragan
Section VIII Partitioning
Chapter 30 Graph and Hypergraph Partitioning
829(50)
Sachin B. Patkar
H. Narayanan
Section IX Matroids
Chapter 31 Matroids
879(44)
H. Narayanan
Sachin B. Patkar
Chapter 32 Hybrid Analysis and Combinatorial Optimization
923(22)
H. Narayanan
Section X Probabilistic Methods, Random Graph Models, and Randomized Algorithms
Chapter 33 Probabilistic Arguments in Combinatorics
945(52)
C.R. Subramanian
Chapter 34 Random Models and Analyses for Chemical Graphs
997(14)
Daniel Pascua
Tina M. Kouri
Dinesh P. Mehta
Chapter 35 Randomized Graph Algorithms: Techniques and Analysis
1011(16)
Surender Baswana
Sandeep Sen
Section XI Coping with NP-Completeness
Chapter 36 General Techniques for Combinatorial Approximation
1027(8)
Sartaj Sahni
Chapter 37 ε-Approximation Schemes for the Constrained Shortest Path Problem
1035(6)
Krishnaiyan "KT" Thulasiraman
Chapter 38 Constrained Shortest Path Problem: Lagrangian Relaxation-Based Algorithmic Approaches
1041(22)
Ying Xiao
Krishnaiyan "KT" Thulasiraman
Chapter 39 Algorithms for Finding Disjoint Paths with QoS Constraints
1063(12)
Alex Sprintson
Ariel Orda
Chapter 40 Set-Cover Approximation
1075(4)
Neal E. Young
Chapter 41 Approximation Schemes for Fractional Multicommodity Flow Problems
1079(18)
George Karakostas
Chapter 42 Approximation Algorithms for Connectivity Problems
1097(18)
Ramakrishna Thurimella
Chapter 43 Rectilinear Steiner Minimum Trees
1115(26)
Tao Huang
Evangeline F. Y. Young
Chapter 44 Fixed-Parameter Algorithms and Complexity
1141(56)
Venkatesh Raman
Saket Saurabh
Index 1197
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.