Handbook of graph theory, combinatorial optimization, and algorithms

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. Content: 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 Andras Frank and Tibor Jordan 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 Chinh T. Hoang and R. Sritharan Tree-Structured Graphs Andreas Brandstadt 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 epsilon-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 "Over the past fifty years, graph theory has been one of the most rapidly growing areas of mathematics. Since 1960, more than 10,000 different authors have published papers classifed as graph theory by Math Reviews, and for the past decade, more than 1000 graph theory papers have been published each year. Not surprisingly, this Second Edition is about 450 pages longer than the First Edition, which appeared in 2004. This Handbook is intended to provide as comprehensive a view of graph theory as is feasible in a single volume. Many of our chapters survey areas that have large research communities, with hundreds of active mathematicians, and which could be developed into independent handbooks. The 89 contributors to this volume, 31 of whom are new to this edition, collectively represent perhaps as much as 90% or more of the main topics in pure and applied graph theory. Thirteen of the sections in the Second Edition cover newer topics that did not appear in the First Edition. In order to achieve this kind of comprehensiveness, we challenged our contributors to restrict their expository prose to a bare minimum, by adhering to the ready-reference style of the CRC Handbook series, which emphasizes quick accessibility for the non- expert. We thank the contributors for responding so well to this challenge. The 13 chapters of the Handbook are organized into 65 sections. Within each section, several major topics are presented. For each topic, there are lists of the essential definitions and facts, accompanied by examples, tables, remarks, and in some cases, conjectures and open problems. Each section ends with a bibliography of references tied directly to that section. In many cases, these bibliographies are several pages long"-- Provided by publisher This handbook is the first to present a unified, comprehensive treatment of graph theory, combinatorial optimization, and related algorithmic issues. It covers numerous topics of interest in applications in electrical, communication, computer, social, transportation, biological, and other networks. 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, and design and plan graph structures that lead to certain desirable behavior. In the ten years since the publication of the best-selling first edition, more than 1,000 graph theory papers have been published each year. Reflecting these advances, Handbook of Graph Theory, Second Edition provides comprehensive coverage of the main topics in pure and applied graph theory. This second edition-over 400 pages longer than its predecessor-incorporates 14 new sections. Each chapter includes lists of essential definitions and facts, accompanied by examples, tables, remarks, and, in some cases, conjectures and open problems. A bibliograph