Sparse matrix computations and their I O complexity:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
2012
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| Schlagworte: | |
| Online-Zugang: | Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20121123-1113167-0-6 Inhaltsverzeichnis |
| Beschreibung: | X, 198 S. graph. Darst. |
Internformat
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| 245 | 1 | 0 | |a Sparse matrix computations and their I O complexity |c Gero Greiner |
| 264 | 1 | |c 2012 | |
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Datensatz im Suchindex
| _version_ | 1804151555744595968 |
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| adam_text | CONTENTS
1 INTRODUCTION 1
1.1 MOTIVATION 1
1.2 MODELS OF COMPUTATION 5
1.2.1 THE EXTERNAL MEMORY MODEL (EM OR I/O-MODEL) .... 5
1.2.2 THE IDEAL CACHE-OBLIVIOUS MODEL 7
1.2.3 THE PARALLEL EXTERNAL MEMORY MODEL (PEM) 7
1.2.4 A COMPARISON TO OTHER PARALLEL MODELS 10
1.2.5 THE MAPREDUCE PROGRAMMING PARADIGM 12
1.3 SPARSE MATRIX COMPUTATIONS 14
1.3.1 MEMORY LAYOUTS 15
1.3.2 INTERMEDIATE RESULTS 16
1.4 PREVIOUS WORK 17
1.4.1 MATRIX MULTIPLICATION 17
1.4.2 I/O-MODEL AND PEM MODEL 19
1.5 STRUCTURE AND CONTRIBUTION OF THIS THESIS 22
2 TECHNIQUES 25
2.1 HONG KUNG ROUNDS 27
2.2 LOWER BOUNDS BY COUNTING ARGUMENTS 29
2.2.1 TIME FORWARD ANALYSIS 29
2.2.2 TIME BACKWARD ANALYSIS 31
2.3 LOWER BOUNDS WITH A POTENTIAL FUNCTION 35
2.4 A PARALLEL LOWER BOUND FOR SIMPLE FUNCTIONS 39
2.5 A LOWER BOUND FOR SORTING IN THE COMPARISON MODEL 41
2.6 THE PEM MERGE SORT 44
2.6.1 DENSE MATRIX TRANSPOSITION 47
2.7 BUILDING BLOCKS FOR PARALLEL ALGORITHMS 48
2.7.1 GATHER AND SCATTER TASKS 48
2.7.2 PREFIX SUMS 48
HTTP://D-NB.INFO/1046972995
VIII CONTENTS
2.7.3 RANGE-BOUNDED LOAD-BALANCING 49
2.7.4 CONTRACTION . 50
3 BILINEAR FORMS 51
4 MULTIPLE VECTORS 61
4.1 INTRODUCTION 61
4.2 ALGORITHMS 67
4.2.1 DIRECT ALGORITHM 68
4.2.2 SORTING BASED ALGORITHMS 69
4.2.3 TABLE BASED ALGORITHMS 75
4.3 LOWER BOUNDS 80
4.3.1 COLUMN MAJOR LAYOUT 81
4.3.2 BEST-CASE LAYOUT 85
4.4 CONCLUSION 91
5 SPARSE X DENSE 93
5.1 INTRODUCTION 93
5.2 ALGORITHMS 95
5.2.1 LAYOUTS 96
5.2.2 DIRECT ALGORITHM 97
5.2.3 TILE-BASED ALGORITHM 98
5.2.4 USING DENSE PARTS OF A 100
5.2.5 SMALL INSTANCES 107
5.3 DERANDOMISATION 108
5.4 LOWER BOUNDS 112
5.4.1 CLOSING THE PARAMETER RANGE 116
5.5 CONCLUSION 116
6 SPARSE X SPARSE 119
6.1 INTRODUCTION 119
6.2 ALGORITHMS 122
6.2.1 DIRECT ALGORITHM AND ITS VARIANTS 122
6.2.2 SORTING-BASED ALGORITHM 123
6.2.3 TILE-BASED ALGORITHM 124
6.3 LOWER BOUNDS 125
6.3.1 LOWER BOUND FOR BY COUNTING ARGUMENTS 125
6.3.2 LOWER BOUND FOR A CLASS OF ALGORITHMS 126
6.4 CONCLUSION 137
CONTENTS IX
7 MAPREDUCE 139
7.1 INTRODUCTION 139
7.2 UPPER BOUNDS FOR THE SHUFFLE STEP 143
7.2.1 DIRECT SHUFFLING 144
7.2.2 MAP-DEPENDENT SHUFFLE PART 144
7.2.3 REDUCE-DEPENDENT SHUFFLE PART 146
7.2.4 COMPLETE SORTING/MERGING 148
7.3 LOWER BOUNDS FOR THE SHUFFLE STEP 148
7.3.1 BEST-CASE TO ROW MAJOR LAYOUT WITH MULTIPLE INPUT
PAIRS 150
7.3.2 MIXED COLUMN LAYOUT WITH MULTIPLE OUTPUT PAIRS . . . 154
7.3.3 COLUMN MAJOR LAYOUT WITH MULTIPLE OUTPUT PAIRS . . . 157
7.3.4 BEST-CASE LAYOUT WITH MULTIPLE INPUT AND OUTPUT PAIRS 158
7.3.5 TRANSPOSING BOUND 161
7.4 CONCLUSION 164
8 PERMUTATIONS 165
8.1 BMMC-PERMUTATIONS 167
8.1.1 A SIMPLE ALGORITHM FOR BMMC PERMUTATIONS 169
8.1.2 EXTENSION TO OTHER FIELDS 170
8.2 EXPANDER BLOCK GRAPHS 171
8.2.1 DEFINITIONS 171
8.2.2 AN NON-TRIVIAL EASY EXPANDER 173
8.3 CONCLUSION 179
9 CONCLUSION 181
|
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| discipline | Informatik Mathematik Medizin |
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| spelling | Greiner, Gero Verfasser aut Sparse matrix computations and their I O complexity Gero Greiner 2012 X, 198 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier München, Techn. Univ., Diss., 2012 Matrizenmultiplikation (DE-588)4169129-5 gnd rswk-swf Komplexitätstheorie (DE-588)4120591-1 gnd rswk-swf Schwach besetzte Matrix (DE-588)4056053-3 gnd rswk-swf Speicherbedarf (DE-588)4644078-1 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Matrizenmultiplikation (DE-588)4169129-5 s Schwach besetzte Matrix (DE-588)4056053-3 s Speicherbedarf (DE-588)4644078-1 s Komplexitätstheorie (DE-588)4120591-1 s DE-604 Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:91-diss-20121123-1113167-0-6 http://mediatum.ub.tum.de/node?id=1113167 Verlag kostenfrei Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20121123-1113167-0-6 Resolving-System DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026885015&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Greiner, Gero Sparse matrix computations and their I O complexity Matrizenmultiplikation (DE-588)4169129-5 gnd Komplexitätstheorie (DE-588)4120591-1 gnd Schwach besetzte Matrix (DE-588)4056053-3 gnd Speicherbedarf (DE-588)4644078-1 gnd |
| subject_GND | (DE-588)4169129-5 (DE-588)4120591-1 (DE-588)4056053-3 (DE-588)4644078-1 (DE-588)4113937-9 |
| title | Sparse matrix computations and their I O complexity |
| title_auth | Sparse matrix computations and their I O complexity |
| title_exact_search | Sparse matrix computations and their I O complexity |
| title_full | Sparse matrix computations and their I O complexity Gero Greiner |
| title_fullStr | Sparse matrix computations and their I O complexity Gero Greiner |
| title_full_unstemmed | Sparse matrix computations and their I O complexity Gero Greiner |
| title_short | Sparse matrix computations and their I O complexity |
| title_sort | sparse matrix computations and their i o complexity |
| topic | Matrizenmultiplikation (DE-588)4169129-5 gnd Komplexitätstheorie (DE-588)4120591-1 gnd Schwach besetzte Matrix (DE-588)4056053-3 gnd Speicherbedarf (DE-588)4644078-1 gnd |
| topic_facet | Matrizenmultiplikation Komplexitätstheorie Schwach besetzte Matrix Speicherbedarf Hochschulschrift |
| url | http://mediatum.ub.tum.de/node?id=1113167 https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20121123-1113167-0-6 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026885015&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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