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'Graphs. Such a simple idea. Map a problem onto a graph then solve it by searching over the graph or by exploring the structure of the graph. What could be easier? Turns out, however, that working with graphs is a vast and complex field. Keeping up is challenging. To help keep up, you just need an editor who knows most people working with graphs, and have that editor gather nearly 70 researchers to summarize their work with graphs. The result is the book Massive Graph Analytics.'— Timothy G. Mattson, Senior Principal Engineer, Intel Corp Expertise in massive-scale graph analytics is key for solving real-world grand challenges from healthcare to sustainability to detecting insider threats, cyber defense, and more. This book provides a comprehensive introduction to massive graph analytics, featuring contributions from thought leaders across academia, industry, and government. Massive Graph Analytics will be beneficial to students, researchers, and practitioners in academia, national laboratories, and industry who wish to learn about the state-of-the-art algorithms, models, frameworks, and software in massive-scale graph analytics.

This textbook discusses the design and implementation of basic algebraic graph algorithms, and algebraic graph algorithms for complex networks, employing matroids whenever possible. The text describes the design of a simple parallel matrix algorithm kernel that can be used for parallel processing of algebraic graph algorithms. Example code is presented in pseudocode, together with case studies in Python and MPI. The text assumes readers have a background in graph theory and/or graph algorithms.

This textbook introduces graph algorithms on an intuitive basis followed by a detailed exposition using structured pseudocode, with correctness proofs as well as worst-case analyses. Graph algorithms is a well-established subject in mathematics and computer science. Beyond classical application fields, like approximation, combinatorial optimization, graphics, and operations research, graph algorithms have recently attracted increased attention from computational biology, bioinformatics, and computational chemistry. Centered around the fundamental issue of graph isomorphism, this book goes beyond classical graph problems of shortest paths, spanning trees, flows in networks, and matchings in bipartite graphs. Advanced algorithmic results and techniques of practical relevance are presented in a coherent and consolidated way. Furthermore, Python code for all algorithms presented is given in a appendix. Numerous illustrations, examples, problems, exercises, and a comprehensive bibliography support students and professionals in using the book as a text and source of reference.

Covering network designs, discrete convex analysis, facility location and clustering problems, matching games, and parameterized complexity, this book discusses theoretical aspects of combinatorial optimization and graph algorithms. Contributions are by renowned researchers who attended NII Shonan meetings on this essential topic. The collection contained here provides readers with the outcome of the authors'research and productive meetings on this dynamic area, ranging from computer science and mathematics to operations research. Networks are ubiquitous in today's world: the Web, online social networks, and search-and-query click logs can lead to a graph that consists of vertices and edges. Such networks are growing so fast that it is essential to design algorithms to work for these large networks. Graph algorithms comprise an area in computer science that works to design efficient algorithms for networks. Here one can work on theoretical or practical problems where implementation of an algorithm for large networks is needed. In two of the chapters, recent results in graph matching games and fixed parameter tractability are surveyed. Combinatorial optimization is an intersection of operations research and mathematics, especially discrete mathematics, which deals with new questions and new problems, attempting to find an optimum object from a finite set of objects. Most problems in combinatorial optimization are not tractable (i.e., NP-hard). Therefore it is necessary to design an approximation algorithm for them. To tackle these problems requires the development and combination of ideas and techniques from diverse mathematical areas including complexity theory, algorithm theory, and matroids as well as graph theory, combinatorics, convex and nonlinear optimization, and discrete and convex geometry. Overall, the book presents recent progress in facility location, network design, and discrete convex analysis.

Many applications in different domains need to calculate the shortest-path between two points in a graph. In this paper we describe this shortest path problem in detail, starting with the classic Dijkstra's algorithm and moving to more advanced solutions that are currently applied to road network routing, including the use of heuristics and precomputation techniques. Since several of these improvements involve subtle changes to the search space, it may be difficult to appreciate their benefits in terms of time or space requirements. To make methods more comprehensive and to facilitate their comparison, this book presents a single case study that serves as a common benchmark. The paper also compares the search spaces explored by the methods described, both from a quantitative and qualitative point of view, and including an analysis of the number of reached and settled nodes by different methods for a particular topology. Table of Contents: List of Figures / List of Tables / Acknowledgments / Introduction / Graph Theory Basics / Classical Algorithms / Hierarchical Preprocessing-Dependent Approaches / Non-Hierarchical Preprocessing-Dependent Approaches / Analysis and Comparison of Approaches / Conclusions / Bibliography / Authors'Biographies

This book contains Volume 8 of the Journal of Graph Algorithms and Applications (JGAA). JGAA is a peer-reviewed scientific journal devoted to the publication of high-quality research papers on the analysis, design, implementation, and applications of graph algorithms. Areas of interest include computational biology, computational geometry, computer graphics, computer-aided design, computer and interconnection networks, constraint systems, databases, graph drawing, graph embedding and layout, knowledge representation, multimedia, software engineering, telecommunications networks, user interfaces and visualization, and VLSI circuit design.Graph Algorithms and Applications 5 presents contributions from prominent authors and includes selected papers from the Tenth International Symposium on Graph Drawing (GD 2002). All papers in the book have extensive diagrams and offer a unique treatment of graph algorithms focusing on the important applications.

This book contains Volume 7 of the Journal of Graph Algorithms and Applications (JGAA). JGAA is a peer-reviewed scientific journal devoted to the publication of high-quality research papers on the analysis, design, implementation, and applications of graph algorithms. Areas of interest include computational biology, computational geometry, computer graphics, computer-aided design, computer and interconnection networks, constraint systems, databases, graph drawing, graph embedding and layout, knowledge representation, multimedia, software engineering, telecommunications networks, user interfaces and visualization, and VLSI circuit design.Graph Algorithms and Applications 4 presents contributions from prominent authors and includes selected papers from (a) the Seventh International Workshop on Algorithms and Data Structures (WADS 2001) and (b) the 2001 Symposium on Graph Drawing (GD 2001). All papers in the book have extensive diagrams and offer a unique treatment of graph algorithms focusing on the important applications.