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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 brings together the knowledge accumulated during many years to extract both theoretical foundations of graph partitioning and its main applications.
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 brings together the knowledge accumulated during many years to extract both theoretical foundations of graph partitioning and its main applications.
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Autorenporträt
Charles-Edmond Bichot is Associate Professor at École Centrale de Lyon in France. His work always focuses on the graph partitioning optimization problem and its applications. Patrick Siarry is Professor in automatics and informatics at Paris-Est University in France. His main research interests are the applications of new stochastic global optimization heuristics to various engineering fields.
Inhaltsangabe
Introduction xiii Charles-Edmond Bichot, Patrick Siarry Chapter 1. General Introduction to Graph Partitioning 1 Charles-Edmond Bichot 1.1. Partitioning 1 1.2. Mathematical notions 2 1.3. Graphs 4 1.4. Formal description of the graph partitioning problem 8 1.5. Objective functions for graph partitioning 11 1.6. Constrained graph partitioning 13 1.7. Unconstrained graph partitioning 14 1.8. Differences between constrained and unconstrained partitioning 16 1.9. From bisection to k-partitioning: the recursive bisection method 17 1.10. NP-hardness of graph partitioning optimization problems 19 1.11. Conclusion 22 1.12. Bibliography 22 Part 1: Graph Partitioning for Numerical Analysis 27 Chapter 2. A Partitioning Requiring Rapidity and Quality: The Multilevel Method and Partitions Refinement Algorithms 29 Charles-Edmond Bichot 2.1. Introduction 29 2.2. Principles of the multilevel method 30 2.3. Graph coarsening 33 2.4. Partitioning of the coarsened graph 37 2.5. Uncoarsening and partitions refinement 40 2.6. The spectral method 52 2.7. Conclusion 59 2.8. Bibliography 60 Chapter 3. Hypergraph Partitioning 65 Cédric Chevalier 3.1. Definitions and metrics 65 3.2. Connections between graphs, hypergraphs, and matrices 67 3.3. Algorithms for hypergraph partitioning 68 3.4. Purpose 72 3.5. Conclusion 77 3.6. Software references 78 3.7. Bibliography 78 Chapter 4. Parallelization of Graph Partitioning 81 François Pellegrini 4.1. Introduction 81 4.2. Distributed data structures 84 4.3. Parallelization of the coarsening phase 87 4.4. Folding 93 4.5. Centralization 95 4.6. Parallelization of the refinement phase 96 4.7. Experimental results 107 4.8. Conclusion 111 4.9. Bibliography 111 Chapter 5. Static Mapping of Process Graphs 115 François Pellegrini 5.1. Introduction 115 5.2. Static mapping models 116 5.3. Exact algorithms 121 5.4. Approximation algorithms 123 5.5. Conclusion 133 5.6. Bibliography 134 Part 2: Optimization Methods for Graph Partitioning 137 Chapter 6. Local Metaheuristics and Graph Partitioning 139 Charles-Edmond Bichot 6.1. General introduction to metaheuristics 140 6.2. Simulated annealing 141 6.3. Iterated local search 149 6.4. Other local search metaheuristics 158 6.5. Conclusion 159 6.6. Bibliography 159 Chapter 7. Population-based Metaheuristics, Fusion-Fission and Graph Partitioning Optimization 163 Charles-Edmond Bichot 7.1. Ant colony algorithms 163 7.2. Evolutionary algorithms 165 7.3. The fusion-fission method 182 7.4. Conclusion 195 7.5. Acknowledgments 196 7.6. Bibliography 196 Chapter 8. Partitioning Mobile Networks into Tariff Zones 201 Mustapha Oughdi, Sid Lamrous, Alexandre Caminada 8.1. Introduction 201 8.2. Spatial division of the network 208 8.3. Experimental results 220 8.4. Conclusion 222 8.5. Bibliography 223 Chapter 9. Air Traffic Control Graph Partitioning Application 225 Charles-Edmond Bichot, Nicolas Durand 9.1. Introduction 225 9.2. The problem of dividing up the airspace 227 9.3. Modeling the problem 231 9.4. Airspace partitioning: towards a new optimization metaheuristic 237 9.5. Division of the central European airspace 240 9.6. Conclusion 246 9.7. Acknowledgments 247 9.8. Bibliography 247 Part 3: Other Approaches to Graph Partitioning 249 Chapter 10. Application of Graph Partitioning to Image Segmentation 251 Amir Nakib, Laurent Najman, Hugues Talbot, Patrick Siarry 10.1. Introduction 251 10.2. The image viewed in graph form 251 10.3. Principle of image segmentation using graphs 254 10.4. Image segmentation via maximum flows 257 10.5. Unification of segmentation methods via graph theory 265 10.6. Conclusions and perspectives 269 10.7. Bibliography 271 Chapter 11. Distances in Graph Partitioning 275 Alain Guénoche 11.1. Introduction 275 11.2. The Dice distance 276 11.3. Pons-Latapy distance 281 11.4. A partitioning method for distance arrays 283 11.5. A simulation protocol 286 11.6. Conclusions 292 11.7. Acknowledgments 293 11.8. Bibliography 293 Chapter 12. Detection of Disjoint or Overlapping Communities in Networks 297 Jean-Baptiste Angelelli, Alain Guénoche, Laurence Reboul 12.1. Introduction 297 12.2. Modularity of partitions and coverings 299 12.3. Partitioning method 301 12.4. Overlapping partitioning methods 307 12.5. Conclusion 311 12.6. Acknowledgments 312 12.7. Bibliography 312 Chapter 13. Multilevel Local Optimization of Modularity 315 Thomas Aynaud, Vincent D. Blondel, Jean-Loup Guillaume and Renaud Lambiotte 13.1. Introduction 315 13.2. Basics of modularity 317 13.3. Modularity optimization 319 13.4. Validation on empirical and artificial graphs 327 13.5. Discussion 333 13.6. Conclusion 341 13.7. Acknowledgments 342 13.8. Bibliography 342 Appendix. The Main Tools and Test Benches for Graph Partitioning 347 Charles-Edmond Bichot A.1. Tools for constrained graph partitioning optimization 348 A.2. Tools for unconstrained graph partitioning optimization 350 A.3. Graph partitioning test benches 351 A.4. Bibliography 354 Glossary 357 List of Authors 361 Index 365
