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Shape optimized graph partitioning / von Stefan Schamberger. 2006
Content
Introduction
Graph Partitioning
Problem Definition
Analytical Bounds
Global Methods
Spectral Bisectioning
Linear Orderings
Space-Filling Curves
Graph-Filling Curves
Local Heuristics
Kernighan-Lin
Helpful-Sets
The Multilevel Scheme
Matching Algorithms
Partitioning Libraries
Graph Repartitioning
The PARTY Graph Partitioning Library
An Improved Evaluation Scheme
Implementation Enhancements
Weight Limited Coarsening
The Improved Helpful-Set Implementation
Experimental Results
Balanced Partitionings
Less Restrictively Balanced Partitionings
Recursive vs. Direct Partitioning
Upshot
Diffusion
The General Diffusion Scheme
Further Results on Diffusion
Overrelaxation and Generalization
Inhomogeneous Networks
Optimal diffusion matrices
Dynamic Networks
Shape Optimized Partitioning
Motivation
The Bubble Framework
Previous Implementations
Diffusion Based Mechanisms
The Limited First Order Scheme
The First Order Scheme with Absolute Draining
The First Order Scheme with Constant Draining
Numerical Stability by Influence Range Reduction
Balancing
Scale Balancing
Greedy Balancing
Smoothing
The Flux Heuristic
Implementation
Partial Graph Coarsening
Domain Decomposition and Domain Sharing
Multilevel Strategy
Experiments
Metrics and Norms
Benchmarks
Graph Sequences and Transitions
A Basic Sequence Generator
Test-set Sequences
Numerical Results
Graph Partitioning
Graph Repartitioning
Application in PadFEM
Upshot
Conclusion
Bibliography
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