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Graph Partitioning.
Graph partitioning is a theoretical subject with applications in many areas, principally: numerical analysis, programs mapping onto parallel architectures, image segmentation, VLSI design. During the last 40 years, the literature has strongly increased and big improvements have been made. This book...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
London :
Wiley,
2013.
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| Colección: | ISTE.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Graph Partitioning; Title Page; Copyright Page; Table of Contents; Introduction; Chapter 1. General Introduction to Graph Partitioning; 1.1. Partitioning; 1.2. Mathematical notions; 1.3. Graphs; 1.4. Formal description of the graph partitioning problem; 1.5. Objective functions for graph partitioning; 1.6. Constrained graph partitioning; 1.7. Unconstrained graph partitioning; 1.8. Differences between constrained and unconstrained partitioning; 1.9. From bisection to k-partitioning: he recursive bisection method.
- 1.9.1. Creating a partition with a number of parts a power of 2, from a graph bisection algorithm1.9.2. Creating a k-partition from a graph bisection algorithm using the partitioning balance; 1.10. NP-hardness of graph partitioning optimization problems; 1.10.1. The case of constrained graph partitioning; 1.10.2. The case of unconstrained graph partitioning; 1.11. Conclusion; 1.12. Bibliography; PART 1: GRAPH PARTITIONING FOR NUMERICAL ANALYSIS; Chapter 2. A Partitioning Requiring Rapidity and Quality: The Multilevel Method and Partitions Refinement Algorithms; 2.1. Introduction.
- 2.2. Principles of the multilevel method2.3. Graph coarsening; 2.3.1. Introduction; 2.3.2. Graph matching; 2.3.3. Hendrickson-Leland coarsening algorithm; 2.3.4. The Heavy Edge Matching (HEM) algorithm; 2.4. Partitioning of the coarsened graph; 2.4.1. State-of-the-art partitioning methods; 2.4.2. Region growing methods; 2.5. Uncoarsening and partitions refinement; 2.5.1. Presentation of the uncoarsening and refinement phase; 2.5.2. The Kernighan-Lin algorithm; 2.5.3. Fiduccia-Mattheyses implementation; 2.5.4. Adaptation to direct k-partitioning; 2.5.5. Global Kernighan-Lin Refinement.
- 2.5.6. The Walshaw-Cross refinement algorithm2.6. The spectral method; 2.6.1. Presentation; 2.6.2. Some results of numerical system; 2.6.3. Finding the eigenvalues of the Laplacian matrix of a graph; 2.6.4. Lower bound for constrained graph partitioning; 2.6.5. Spectral methods for contrained partitioning; 2.6.6. Spectral methods for unconstrained graph partitioning; 2.6.7. Problems and improvements; 2.7. Conclusion; 2.8. Bibliography; Chapter 3. Hypergraph Partitioning; 3.1. Definitions and metrics; 3.1.1. Hypergraph and partitioning; 3.1.2. Metrics for hypergraph partitioning.
- 3.2. Connections between graphs, hypergraphs, and matrices3.3. Algorithms for hypergraph partitioning; 3.3.1. Coarsening; 3.3.2. Initial partitioning and uncoarsening and refinement; 3.3.3. Uncoarsening and refinement; 3.4. Purpose; 3.4.1. Hypergraph partitioning benefits; 3.4.2. Matrix partitioning; 3.4.3. Practical results; 3.4.4. Repartitioning; 3.4.5. Use of hypergraphs within a mesh partitioning context; 3.4.6. Other applications; 3.5. Conclusion; 3.6. Software references; 3.7. Bibliography; Chapter 4. Parallelization of Graph Partitioning; 4.1. Introduction; 4.1.1. Need for parallelism.