Graph Algorithms in the Language of Linear Algebra
Society for Industrial & Applied Mathematics,U.S. (Verlag)
978-0-89871-990-1 (ISBN)
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.
Jeremy Kepner is a senior technical staff member at the Massachusetts Institute of Technology Lincoln Laboratory. His research focuses on the development of advanced libraries for the application of massively parallel computing to a variety of data intensive signal processing problems on which he has published many articles. John Gilbert is a SIAM Fellow and Professor of Computer Science at the University of California, Santa Barbara. His research interests are in combinatorial scientific computing, high-performance graph algorithms, tools and software for computational science and engineering, numerical linear algebra and distributed sensing and control.
Preface; Part I. Algorithms: 1. Graphs and matrices; 2. Linear algebraic notation and definitions; 3. Connected components and minimum paths; 4. Some graph algorithms in an array-based language; 5. Fundamental graph algorithms; 6. Complex graph algorithms; 7. Multilinear algebra for analyzing data with multiple linkages; 8. Subgraph detection; Part II. Data: 9. Kronecker graphs; 10. The Kronecker theory of power law graphs; 11. Visualizing large Kronecker graphs; Part III. Computation: 12. Large-scale network analysis; 13. Implementing sparse matrices for graph algorithms; 14. New ideas in sparse matrix-matrix multiplication; 15. Parallel mapping of sparse computations; 16. Fundamental questions in the analysis of large graphs; Index.
| Verlagsort | New York |
|---|---|
| Sprache | englisch |
| Maße | 182 x 261 mm |
| Gewicht | 990 g |
| Themenwelt | Informatik ► Theorie / Studium ► Algorithmen |
| ISBN-10 | 0-89871-990-9 / 0898719909 |
| ISBN-13 | 978-0-89871-990-1 / 9780898719901 |
| Zustand | Neuware |
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