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Graph Algorithms in the Language of Linear Algebra by John Gilbert, Jeremy Kepner (Hardcover, 2011)

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To improve the computational performance of graph algorithms, researchers have proposed a shift to a parallel computing paradigm. This linear algebraic approach is widely accessible to scientists and engineers who may not be formally trained in computer science.

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The field of graph algorithms has become one of the pillars of theoretical computer science, informing research in such diverse areas as combinatorial optimization, complexity theory and topology. To improve the computational performance of graph algorithms, researchers have proposed a shift to a parallel computing paradigm. This book addresses the challenges of implementing parallel graph algorithms 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.