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Graphs, Algorithms, and Optimization is a comprehensive book that features a clear explanation of modern graph theory in a rigorous yet approachable way. Suitable for use as a textbook in either mathematics or computer science courses, it is designed to present graph theory from an algorithmic point of view, allowing for a variety of technical applications. It includes useful programming techniques to solve graph theory problems, and applicable data structures to show how algorithms can be programmed. Additional coverage is provided on discrete optimization and its connection to graph theory, algorithmic complexity and efficiency, NP- completeness, and linear optimization.

Graph algorithms --- Algorithmes de graphes --- Graph algorithms.

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Algorithmic graph theory has been expanding at an extremely rapid rate since the middle of the twentieth century, in parallel with the growth of computer science and the accompanying utilization of computers, where efficient algorithms have been a prime goal. This book presents material on developments on graph algorithms and related concepts that will be of value to both mathematicians and computer scientists, at a level suitable for graduate students, researchers and instructors. The fifteen expository chapters, written by acknowledged international experts on their subjects, focus on the application of algorithms to solve particular problems. All chapters were carefully edited to enhance readability and standardize the chapter structure as well as the terminology and notation. The editors provide basic background material in graph theory, and a chapter written by the book's Academic Consultant, Martin Charles Golumbic (University of Haifa, Israel), provides background material on algorithms as connected with graph theory.

Graph algorithms. --- Graph theory.

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Deep learning on graphs has become one of the hottest topics in machine learning. The book consists of four parts to best accommodate our readers with diverse backgrounds and purposes of reading. Part 1 introduces basic concepts of graphs and deep learning; Part 2 discusses the most established methods from the basic to advanced settings; Part 3 presents the most typical applications including natural language processing, computer vision, data mining, biochemistry and healthcare; and Part 4 describes advances of methods and applications that tend to be important and promising for future research. The book is self-contained, making it accessible to a broader range of readers including (1) senior undergraduate and graduate students; (2) practitioners and project managers who want to adopt graph neural networks into their products and platforms; and (3) researchers without a computer science background who want to use graph neural networks to advance their disciplines.

Machine learning --- Graph algorithms --- Machine learning. --- Graph algorithms.

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Quantitative methods (economics) --- Graph algorithms. --- Graph theory

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"Graphs are among the most important abstract data types in computer science, and the algorithms that operate on them are critical to modern life. Graphs have been shown to be powerful tools for modeling complex problems because of their simplicity and generality. Graph algorithms are one of the pillars of mathematics, informing research in such diverse areas as combinatorial optimization, complexity theory, and topology. Algorithms on graphs are applied in many ways in today's world-from Web rankings to metabolic networks, from finite element meshes to semantic graphs. The current exponential growth in graph data has forced a shift to parallel computing for executing graph algorithms. Implementing parallel graph algorithms and achieving good parallel performance have proven difficult. This book addresses these challenges by exploiting the well-known duality between a canonical representation of graphs as abstract collections of vertices and edges and a sparse adjacency matrix representation. This linear algebraic approach is widely accessible to scientists and engineers who may not be formally trained in computer science. The authors show how to leverage existing parallel matrix computation techniques and the large amount of software infrastructure that exists for these computations to implement efficient and scalable parallel graph algorithms. The benefits of this approach are reduced algorithmic complexity, ease of implementation, and improved performance. Graph Algorithms in the Language of Linear Algebra is the first book to cover : graph algorithms accessible to engineers and scientists not trained in computer science but having a strong linear algebra background, enabling them to quickly understand and apply graph algorithms; array-based graph algorithms, showing readers how to express canonical graph algorithms using a highly elegant and efficient array notation and how to tap into the large range of tools and techniques that have been built for matrices and tensors; parallel array-based algorithms, demonstrating with examples how to easily implement parallel graph algorithms using array-based approaches, which enables readers to address much larger graph problems; array-based theory for analyzing graphs, providing a template for using array-based constructs to develop new theoretical approaches for graph analysis. This book is suitable as the primary text for a class on linear algebraic graph algorithms and as either the primary or supplemental text for a class on graph algorithms for engineers and scientists without training in computer science." [Publisher]

Graph algorithms. --- Algebras, Linear. --- Algèbre linéaire.