Fast parallel algorithms for graph matching problems:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Clarendon Press
1998
|
| Series: | Oxford lecture series in mathematics and its applications
9 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 212 S. graph. Darst. |
| ISBN: | 0198501625 |
Staff View
MARC
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| 100 | 1 | |a Karpiński, Marek |d 1948- |e Verfasser |0 (DE-588)115476032 |4 aut | |
| 245 | 1 | 0 | |a Fast parallel algorithms for graph matching problems |c Marek Karpinski and Wojciech Rytter |
| 264 | 1 | |a Oxford [u.a.] |b Clarendon Press |c 1998 | |
| 300 | |a XI, 212 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Oxford lecture series in mathematics and its applications |v 9 | |
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| 650 | 7 | |a appariement |2 inriac | |
| 650 | 7 | |a théorie graphe |2 inriac | |
| 650 | 4 | |a Graph theory | |
| 650 | 4 | |a Matching theory | |
| 650 | 4 | |a Parallel algorithms | |
| 650 | 0 | 7 | |a Graphentheorie |0 (DE-588)4113782-6 |2 gnd |9 rswk-swf |
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Record in the Search Index
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| adam_text | Contents
1 Introduction 1
1.1 Matchings in graphs: terminology, examples 1
1.2 The model of parallel computations: PRAM 4
1.3 The complexity classes NC and RNC 6
1.4 Bibliographic notes 7
2 Combinatorial tools 8
2.1 Augmenting paths 8
2.2 Deficiencies and witness sets 11
2.3 Bipartite graphs and their witness sets 13
2.4 Tutte s theorem and witness sets in general graphs 15
2.5 Odd set covers 19
2.6 Good edges lemma 20
2.7 Bibliographic notes 21
3 Three sequential algorithms 22
3.1 Hopcroft Karp algorithm 23
3.2 Edmonds algorithm and blossoms 26
3.3 Structural algorithm (no blossoms) 32
3.4 Bibliographic notes 40
4 Probabilistic tools 41
4.1 Probabilistic tools 41
4.2 The isolating theorem 42
4.3 The redundancy theorem 45
4.4 Randomized handshaking 48
4.5 Estimating the probability of nonzero sums 50
4.6 Removing a large proportion of elements 51
4.7 Derandomization 52
4.8 Bibliographic notes 54
5 Algebraic tools 55
5.1 Determinants versus permanents 55
5.2 Symbolic polynomials of set families 57
5.3 Nonzero test and partial interpolation of polynomials 60
5.4 Sparse polynomials 63
5.5 Randomized computation of the smallest degree 65
5.6 Ranks of matrices 67
5.7 NC computation of determinants 68
5.8 Bibliographic notes 72
6 Maximum cardinality matchings 73
6.1 Constructing black box polynomials 73
6.2 Bimatchings and Pfaffians 79
6.3 Applying partial interpolation 83
6.4 Graphs with a small number of perfect matchings 85
6.5 From Monte Carlo to Las Vegas 86
6.6 The shrinking algorithm 88
6.7 Application of the smallest degree algorithm 90
6.8 Bibliographic notes 93
7 Inclusion maximal matchings 94
7.1 Deterministic algorithm for maximal matchings 94
7.2 An application of randomized handshaking 101
7.3 Bibliographic notes 103
8 Maximal independent sets 104
8.1 Two algorithms of Luby 104
8.2 Deterministic algorithm for maximal independent sets 107
8.3 Maximal independent sets in hypergraphs 111
8.4 Maximal ^ dependent sets 112
8.5 Bibliographic notes 115
9 Four easy subclasses of graphs 116
9.1 Trees 116
9.2 Dense graphs 117
9.3 Regular bipartite graphs 120
9.4 Claw free graphs and pseudo matchings 124
9.5 Bibliographic notes 130
10 Families of intervals 131
10.1 The greedy sequential algorithm 132
10.2 Left justification of set families 133
10.3 The parallel algorithm for the general case 136
10.4 Bibliographic notes 138
11 Parallel algorithms for / matchings 139
11.1 ft/VC algorithm for maximum / matchings 140
11.2 Simple /WC algorithm for maximal / matchings 141
11.3 Deterministic JVC algorithm for maximal / matchings 144
11.4 Bibliographic notes 150
12 Parallelization of sequential algorithms 151
12.1 Parallelizing the Hopcroft Karp algorithm 151
12.2 Parallel implementation of BFS and Disjoint.Paths 152
12.3 yVC approximation of maximum matching 156
12.4 Bipartite expander graphs 158
12.5 Applying the planar separator theorem 159
12.6 Parallel version of the Edmonds algorithm 162
12.7 Bibliographic notes 163
13 Pfaffians, counting the number of matchings, and pla¬
nar graphs 164
13.1 Pfaffians of graphs 164
13.2 Skew symmetric determinants and Pfaffians 165
13.3 Pfaffians and counting the number of perfect matchings 166
13.4 Bibliographic notes 170
14 Basic applications of parallel matching 171
14.1 The subtree isomorphism problem 171
14.2 Maximum flows and disjoint paths 175
14.3 Parallel construction of DFS trees 180
14.4 Bibliographic notes 186
15 More applications 187
15.1 Unary Chinese postman problem 187
15.2 Two processor scheduling 188
15.3 Cycle covers and shortest superstrings 190
15.4 The | approximation of the metric TSP 192
15.5 The bandwidth problem 193
15.6 Spanning 3 hypertrees and approximating Steiner tree 195
15.7 Bibliographic notes 197
Bibliography 198
Index 207
|
| any_adam_object | 1 |
| author | Karpiński, Marek 1948- Rytter, Wojciech |
| author_GND | (DE-588)115476032 |
| author_facet | Karpiński, Marek 1948- Rytter, Wojciech |
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| dewey-full | 511.5028551 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.5028551 |
| dewey-search | 511.5028551 |
| dewey-sort | 3511.5028551 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:19:45Z |
| institution | BVB |
| isbn | 0198501625 |
| language | English |
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| physical | XI, 212 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Clarendon Press |
| record_format | marc |
| series | Oxford lecture series in mathematics and its applications |
| series2 | Oxford lecture series in mathematics and its applications Oxford Science publications |
| spelling | Karpiński, Marek 1948- Verfasser (DE-588)115476032 aut Fast parallel algorithms for graph matching problems Marek Karpinski and Wojciech Rytter Oxford [u.a.] Clarendon Press 1998 XI, 212 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford lecture series in mathematics and its applications 9 Oxford Science publications Algorithmes parallèles ram Couplage, Théorie du ram Graphes, Théorie des ram algorithme parallèle inriac algorithme rapide inriac appariement inriac théorie graphe inriac Graph theory Matching theory Parallel algorithms Graphentheorie (DE-588)4113782-6 gnd rswk-swf Matching-Problem (DE-588)4198185-6 gnd rswk-swf Paralleler Algorithmus (DE-588)4193615-2 gnd rswk-swf Graphentheorie (DE-588)4113782-6 s Matching-Problem (DE-588)4198185-6 s DE-604 Paralleler Algorithmus (DE-588)4193615-2 s Rytter, Wojciech Verfasser aut Oxford lecture series in mathematics and its applications 9 (DE-604)BV009910017 9 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008112072&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Karpiński, Marek 1948- Rytter, Wojciech Fast parallel algorithms for graph matching problems Oxford lecture series in mathematics and its applications Algorithmes parallèles ram Couplage, Théorie du ram Graphes, Théorie des ram algorithme parallèle inriac algorithme rapide inriac appariement inriac théorie graphe inriac Graph theory Matching theory Parallel algorithms Graphentheorie (DE-588)4113782-6 gnd Matching-Problem (DE-588)4198185-6 gnd Paralleler Algorithmus (DE-588)4193615-2 gnd |
| subject_GND | (DE-588)4113782-6 (DE-588)4198185-6 (DE-588)4193615-2 |
| title | Fast parallel algorithms for graph matching problems |
| title_auth | Fast parallel algorithms for graph matching problems |
| title_exact_search | Fast parallel algorithms for graph matching problems |
| title_full | Fast parallel algorithms for graph matching problems Marek Karpinski and Wojciech Rytter |
| title_fullStr | Fast parallel algorithms for graph matching problems Marek Karpinski and Wojciech Rytter |
| title_full_unstemmed | Fast parallel algorithms for graph matching problems Marek Karpinski and Wojciech Rytter |
| title_short | Fast parallel algorithms for graph matching problems |
| title_sort | fast parallel algorithms for graph matching problems |
| topic | Algorithmes parallèles ram Couplage, Théorie du ram Graphes, Théorie des ram algorithme parallèle inriac algorithme rapide inriac appariement inriac théorie graphe inriac Graph theory Matching theory Parallel algorithms Graphentheorie (DE-588)4113782-6 gnd Matching-Problem (DE-588)4198185-6 gnd Paralleler Algorithmus (DE-588)4193615-2 gnd |
| topic_facet | Algorithmes parallèles Couplage, Théorie du Graphes, Théorie des algorithme parallèle algorithme rapide appariement théorie graphe Graph theory Matching theory Parallel algorithms Graphentheorie Matching-Problem Paralleler Algorithmus |
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