(Ebook) Graph Partitioning 1st Edition by Charles Edmond Bichot, Patrick Siarry ISBN 9781848212336 184821233X

(Ebook) Graph Partitioning 1st Edition by Charles Edmond Bichot, Patrick Siarry ISBN 9781848212336 184821233X

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ISBN 10: 184821233X
ISBN 13: 9781848212336
Author: Charles Edmond Bichot, Patrick Siarry

(Ebook) Graph Partitioning 1st Edition Table of contents:

1. Foundations of 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
1.9.2. Creating a k-partition from a graph bisection algorithm using the partitioning balance
1.10.1. The case of constrained graph partitioning
1.10.2. The case of unconstrained graph partitioning
1.12. Bibliography

PART 1: Graph Partitioning for Numerical Analysis

2. Multilevel Methods
2.1. Introduction
2.2. Principles of the multilevel method
2.3.1. Introduction
2.3.3. Hendrickson–Leland coarsening algorithm
2.3.4. The Heavy Edge Matching (HEM) algorithm
2.4.1. State-of-the-art partitioning methods
2.4.2. Region growing methods
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 algorithm
2.6.2. Some results of numerical system
2.6.3. Finding the eigenvalues of the Laplacian matrix of a graph
2.6.5. Spectral methods for constrained partitioning
2.6.6. Spectral methods for unconstrained graph partitioning
2.6.7. Problems and improvements
2.7. Conclusion
2.8. Bibliography

3. Hypergraph Partitioning
3.1.1. Hypergraph and partitioning
3.2. Connections between graphs, hypergraphs, and matrices
3.3. Algorithms for hypergraph partitioning
3.3.1. Coarsening
3.3.3. Uncoarsening and refinement
3.4.1. Hypergraph partitioning benefits
3.4.2. Matrix partitioning
3.4.3. Practical results
3.4.6. Other applications
3.5. Conclusion
3.7. Bibliography

4. Parallel Graph Partitioning
4.1.1. Need for parallelism
4.1.2. Multilevel framework
4.2. Distributed data structures
4.3.2. Parallel matching algorithms
4.3.3. Collision reduction at process level
4.3.4. Collision reduction at vertex level
4.4. Folding
4.5. Centralization
4.6.1. Parallelization of local refinement methods
4.6.2. Band graphs
4.6.3. Multi-centralization
4.6.4. Parallelization of global refinement methods
4.7. Experimental results
4.9. Bibliography

5. Partitioning for Heterogeneous Architectures
5.1. Introduction
5.2.1. Cost functions
5.2.2. Heterogeneity of target architectures
5.3. Exact algorithms
5.4.1. Global methods
5.4.2. Recursive methods
5.5. Conclusion
5.6. Bibliography

PART 2: Optimization Methods for Graph Partitioning

6. Local Metaheuristics
6.1. General introduction to metaheuristics
6.2. Simulated annealing
6.2.1. Description of simulated annealing
6.2.2. Adaptation to graph bisection
6.2.3. Generalization to k-partitioning
6.2.4. Assessment
6.3.1. Iterated local search
6.3.2. Simple adaptation to graph partitioning
6.3.3. Iterated local search and the multilevel method
6.4.1. Greedy algorithms
6.6. Bibliography

7. Evolutionary and Swarm Methods
7.1. Ant colony algorithms
7.2.1. Genetic algorithms
7.2.2. Standard genetic algorithm process
7.2.3. Adaptation to bisection (BUI and MOON)
7.2.4. Multilevel evolutionary algorithm (Soper–Walshaw–Cross)
7.2.5. Other evolutionary adaptations
7.3.1. Introduction
7.3.2. Fusion-fission method principles
7.3.3. Algorithm
7.3.4. Selection of multilevel algorithm
7.3.5. Creation of part-number sequences
7.3.6. Selection of refinement algorithm
7.3.7. Evaluation
7.4. Conclusion
7.6. Bibliography

8. Space Division Optimization
8.1.1. Scheduled rating model
8.1.2. Rating model for a network
8.2.1. Definitions
8.2.2. Space division problem formalization
8.2.3. Solving space division using genetic algorithms
8.3. Experimental results
8.4. Conclusion
8.5. Bibliography

9. Airspace Partitioning
9.1. Introduction
9.2. The problem of dividing airspace
9.2.1. Functional airspace blocks in Europe
9.2.2. Functional block in central Europe
9.3.1. Control workload in a sector
9.3.3. Constraints on qualification areas and control centers
9.3.4. Analysis of European air traffic data
9.3.5. Graph of European air traffic and adaptation
9.4. New optimization metaheuristic
9.5. Division of central European airspace
9.6. Conclusion
9.8. Bibliography

PART 3: Other Approaches to Graph Partitioning

10. Image Segmentation via Graphs
10.2. Images viewed as graphs
10.3. Principles of graph-based segmentation
10.3.1. Choice of arc weights
10.4.1. Maximum flows for energy minimization
10.4.2. Minimal geodesics and surfaces
10.4.3. Minimum geodesics/surfaces via max flows
10.5. Unified segmentation methods
10.6. Conclusions and perspectives
10.7. Bibliography

11. Distance-Based Partitioning
11.1. Introduction
11.2. Dice distance
11.2.1. Extensions to weighted graphs
11.3. Pons–Latapy distance
11.4. Method for partitioning distance arrays
11.5.2. Quality of computed partition
11.5.3. Results
11.6. Conclusions
11.8. Bibliography

12. Overlapping and Modularity-Based Methods
12.1. Introduction
12.2. Modularity of partitions and coverings
12.3. Partitioning method
12.3.1. Fusion/fission of clusters
12.3.3. Simulations
12.4. Overlapping partitioning methods
12.4.1. Fusion of overlapping classes
12.4.2. Simulations
12.5. Conclusion
12.7. Bibliography

13. Community Detection and Modularity Algorithms
13.1. Introduction
13.2. Basics of modularity
13.3.1. Existing methods
13.3.2. Known limitations
13.3.3. Louvain method
13.3.4. Modularity increase
13.3.5. Algorithm convergence
13.4. Validation on artificial and empirical graphs
13.4.1. Artificial graphs
13.4.2. Empirical graphs
13.5.1. Influence of vertex order
13.5.2. Intermediate communities
13.5.3. Possible improvements
13.5.4. Known uses
13.6. Conclusion
13.8. Bibliography

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Tags: Charles Edmond Bichot, Patrick Siarry, Graph Partitioning