Shape optimized graph partitioning:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
2006
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| Subjects: | |
| Online Access: | http://d-nb.info/983282455/34 http://ubdata.uni-paderborn.de/ediss/17/2006/schamber/ Inhaltsverzeichnis |
| Item Description: | Paderborn, Univ., Diss., 2006 |
| Physical Description: | 1 Online-Ressource |
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Record in the Search Index
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| adam_text | Contents
1 Introduction 7
2 Graph Partitioning 11
2.1 Problem Definition 11
2.2 Analytical Bounds 12
2.3 Global Methods 13
2.3.1 Spectral Bisectioning 13
2.3.2 Linear Orderings 14
Space Filling Curves 15
Graph Filling Curves 16
2.4 Local Heuristics 23
2.4.1 Kernighan Lin 23
2.4.2 Helpful Sets 25
2.5 The Multilevel Scheme 25
2.5.1 Matching Algorithms 26
2.5.2 Partitioning Libraries 27
2.6 Graph Repartitioning 28
3 The PARTY Graph Partitioning Library 29
3.1 An Improved Evaluation Scheme 29
3.2 Implementation Enhancements 32
3.2.1 Weight Limited Coarsening 33
3.2.2 The Improved Helpful Set Implementation 33
3.3 Experimental Results 37
3.3.1 Balanced Partitionings 37
3.3.2 Less Restrictively Balanced Partitionings 41
3.3.3 Recursive vs. Direct Partitioning 44
3.4 Upshot 49
4 Diffusion 51
4.1 The General Diffusion Scheme 52
4.2 Further Results on Diffusion 53
4.2.1 Overrelaxation and Generalization 54
4.2.2 Inhomogeneous Networks 54
Optimal diffusion matrices 55
4.2.3 Dynamic Networks 57
5 Shape Optimized Partitioning 63
5.1 Motivation 63
5.2 The Bubble Framework 65
5.2.1 Previous Implementations 66
5.3 Diffusion Based Mechanisms 68
5.3.1 The Limited First Order Scheme 73
5.3.2 The First Order Scheme with Absolute Draining 75
5.3.3 The First Order Scheme with Constant Draining 81
5.3.4 Numerical Stability by Influence Range Reduction 84
5.4 Balancing 87
5.4.1 Scale Balancing 88
5.4.2 Greedy Balancing 89
5.4.3 Smoothing 90
5.5 The Flux Heuristic 91
5.6 Implementation 91
5.6.1 Partial Graph Coarsening 93
5.6.2 Domain Decomposition and Domain Sharing 96
5.6.3 Multilevel Strategy 97
5.7 Experiments 97
5.7.1 Metrics and Norms 98
5.7.2 Benchmarks 99
Graph Sequences and Transitions 100
A Basic Sequence Generator 101
Test set Sequences 103
5.7.3 Numerical Results 106
Graph Partitioning 106
Graph Repartitioning 113
5.7.4 Application in PadFEM 125
5.7.5 Upshot 127
6 Conclusion 129
Bibliography 131
|
| adam_txt |
Contents
1 Introduction 7
2 Graph Partitioning 11
2.1 Problem Definition 11
2.2 Analytical Bounds 12
2.3 Global Methods 13
2.3.1 Spectral Bisectioning 13
2.3.2 Linear Orderings 14
Space Filling Curves 15
Graph Filling Curves 16
2.4 Local Heuristics 23
2.4.1 Kernighan Lin 23
2.4.2 Helpful Sets 25
2.5 The Multilevel Scheme 25
2.5.1 Matching Algorithms 26
2.5.2 Partitioning Libraries 27
2.6 Graph Repartitioning 28
3 The PARTY Graph Partitioning Library 29
3.1 An Improved Evaluation Scheme 29
3.2 Implementation Enhancements 32
3.2.1 Weight Limited Coarsening 33
3.2.2 The Improved Helpful Set Implementation 33
3.3 Experimental Results 37
3.3.1 Balanced Partitionings 37
3.3.2 Less Restrictively Balanced Partitionings 41
3.3.3 Recursive vs. Direct Partitioning 44
3.4 Upshot 49
4 Diffusion 51
4.1 The General Diffusion Scheme 52
4.2 Further Results on Diffusion 53
4.2.1 Overrelaxation and Generalization 54
4.2.2 Inhomogeneous Networks 54
Optimal diffusion matrices 55
4.2.3 Dynamic Networks 57
5 Shape Optimized Partitioning 63
5.1 Motivation 63
5.2 The Bubble Framework 65
5.2.1 Previous Implementations 66
5.3 Diffusion Based Mechanisms 68
5.3.1 The Limited First Order Scheme 73
5.3.2 The First Order Scheme with Absolute Draining 75
5.3.3 The First Order Scheme with Constant Draining 81
5.3.4 Numerical Stability by Influence Range Reduction 84
5.4 Balancing 87
5.4.1 Scale Balancing 88
5.4.2 Greedy Balancing 89
5.4.3 Smoothing 90
5.5 The Flux Heuristic 91
5.6 Implementation 91
5.6.1 Partial Graph Coarsening 93
5.6.2 Domain Decomposition and Domain Sharing 96
5.6.3 Multilevel Strategy 97
5.7 Experiments 97
5.7.1 Metrics and Norms 98
5.7.2 Benchmarks 99
Graph Sequences and Transitions 100
A Basic Sequence Generator 101
Test set Sequences 103
5.7.3 Numerical Results 106
Graph Partitioning 106
Graph Repartitioning 113
5.7.4 Application in PadFEM 125
5.7.5 Upshot 127
6 Conclusion 129
Bibliography 131 |
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| spelling | Schamberger, Stefan Verfasser aut Shape optimized graph partitioning von Stefan Schamberger 2006 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Paderborn, Univ., Diss., 2006 Elektronische Publikation (DE-588)4514269-5 gnd rswk-swf Graphentheoretisches Optimierungsverfahren (DE-588)4158056-4 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Graphentheoretisches Optimierungsverfahren (DE-588)4158056-4 s Elektronische Publikation (DE-588)4514269-5 s DE-604 http://d-nb.info/983282455/34 http://ubdata.uni-paderborn.de/ediss/17/2006/schamber/ HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015506940&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schamberger, Stefan Shape optimized graph partitioning Elektronische Publikation (DE-588)4514269-5 gnd Graphentheoretisches Optimierungsverfahren (DE-588)4158056-4 gnd |
| subject_GND | (DE-588)4514269-5 (DE-588)4158056-4 (DE-588)4113937-9 |
| title | Shape optimized graph partitioning |
| title_auth | Shape optimized graph partitioning |
| title_exact_search | Shape optimized graph partitioning |
| title_exact_search_txtP | Shape optimized graph partitioning |
| title_full | Shape optimized graph partitioning von Stefan Schamberger |
| title_fullStr | Shape optimized graph partitioning von Stefan Schamberger |
| title_full_unstemmed | Shape optimized graph partitioning von Stefan Schamberger |
| title_short | Shape optimized graph partitioning |
| title_sort | shape optimized graph partitioning |
| topic | Elektronische Publikation (DE-588)4514269-5 gnd Graphentheoretisches Optimierungsverfahren (DE-588)4158056-4 gnd |
| topic_facet | Elektronische Publikation Graphentheoretisches Optimierungsverfahren Hochschulschrift |
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