Graph Algorithms in the Language of Linear Algebra

丛 书 名：Software, Environments, and Tools

作     者：Jeremy Kepner John Gilbert 

I S B N：(纸本) 9780898719901 

出 版 社：Society for Industrial and Applied Mathematics 

出 版 年：2011年

主 题 词：graph algorithms network analysis adjacency matrix sparse matrices parallel programming combinatorial scientific computing 

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

摘      要：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 techniq