Algorithmic aspects of graph connectivity:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2008
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Encyclopedia of mathematics and its applications
123 |
| Schlagworte: | |
| Online-Zugang: | Contributor biographical information Publisher description Table of contents only Inhaltsverzeichnis |
| Beschreibung: | Includes index. |
| Beschreibung: | XV, 375 S. graph. Darst. |
| ISBN: | 9780521878647 |
Internformat
MARC
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| 245 | 1 | 0 | |a Algorithmic aspects of graph connectivity |c Hiroshi Nagamochi ; Toshihide Ibaraki |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2008 | |
| 300 | |a XV, 375 S. |b graph. Darst. | ||
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| 490 | 1 | |a Encyclopedia of mathematics and its applications |v 123 | |
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Datensatz im Suchindex
| _version_ | 1804138063926919168 |
|---|---|
| adam_text | Contents
Preface
page
ix
Notation
xi
1
Introduction
1
1.1
Preliminaries of Graph Theory
1
1.2
Algorithms and Complexities
13
1.3
Flows and Cuts
20
1.4
Computing Connectivities
34
1.5
Representations of Cut Structures
45
1.6
Connectivity by Trees
57
1.7
Tree Hypergraphs
60
2
Maximum Adjacency Ordering and Forest Decompositions
65
2.1
Spanning Subgraphs Preserving Connectivity
65
2.2
MA Ordering
73
2.3
3-Edge-Connected Components
86
2.4
2-Approximation Algorithms for Connectivity
100
2.5
Fast Maximum-Flow Algorithms
107
2.6
Testing Chordality
112
3
Minimum Cuts
114
3.1
Pendent Pairs in
MA Orderings
114
3.2
A Minimum-Cut Algorithm
117
3.3
s-Proper ^-Edge-Connected Spanning Subgraphs
119
3.4
A Hierarchical Structure of
MA Orderings
123
3.5
Maximum Flows Between a Pendent Pair
127
3.6
A Generalization of Pendent Pairs
130
3.7
Practically Efficient Minimum-Cut Algorithms
131
4
Cut Enumeration
137
4.1
Enumerating All Cuts
137
4.2
Enumerating Small Cuts
140
vii
viii Contents
4.3
Enumerating Minimum Cuts
145
4.4
Upper Bounds on the Number of Small Cuts
149
5
Cactus Representations
153
5.1
Canonical Forms of Cactus Representations
153
5.2
(s, t )-Cactus
Representations
171
5.3
Constructing Cactus Representations
180
6
Extreme Vertex Sets
191
6.1
Computing Extreme Vertex Sets in Graphs
192
6.2
Algorithm for Dynamic Edges Incident to a Specified Vertex
198
6.3
Optimal Contraction Ordering
200
6.4
Minimum ^-Subpartition Problem
207
7
Edge Splitting
217
7.1
Preliminaries
217
7.2
Edge Splitting in Weighted Graphs
220
7.3
Edge Splitting in Multigraphs
226
7.4
Other Splittings
232
7.5
Detachments
237
7.6
Applications of Splittings
240
8
Connectivity Augmentation
246
8.1
Increasing Edge-Connectivity by One
247
8.2
Star Augmentation
249
8.3
Augmenting Multigraphs
252
8.4
Augmenting Weighted Graphs
254
8.5
More on Augmentation
276
9
Source Location Problems
282
9.1
Source Location Problem Under Edge-Connectivity
Requirements
283
9.2
Source Location Problem Under Vertex-Connectivity
Requirements
295
10
Submodular
and Posimodular Set Functions
304
10.1
Set Functions
304
10.2
Minimizing
Submodular
and Posimodular Functions
306
10.3
Extreme Subsets in
Submodular
and Posimodular Systems
315
10.4
Optimization Problems over
Submodular
and Posimodular
Systems
320
10.5
Extreme Points of Base Polyhedron
336
10.6
Minimum Transversal in Set Systems
342
Bibliography
357
Index
371
|
| adam_txt |
Contents
Preface
page
ix
Notation
xi
1
Introduction
1
1.1
Preliminaries of Graph Theory
1
1.2
Algorithms and Complexities
13
1.3
Flows and Cuts
20
1.4
Computing Connectivities
34
1.5
Representations of Cut Structures
45
1.6
Connectivity by Trees
57
1.7
Tree Hypergraphs
60
2
Maximum Adjacency Ordering and Forest Decompositions
65
2.1
Spanning Subgraphs Preserving Connectivity
65
2.2
MA Ordering
73
2.3
3-Edge-Connected Components
86
2.4
2-Approximation Algorithms for Connectivity
100
2.5
Fast Maximum-Flow Algorithms
107
2.6
Testing Chordality
112
3
Minimum Cuts
114
3.1
Pendent Pairs in
MA Orderings
114
3.2
A Minimum-Cut Algorithm
117
3.3
s-Proper ^-Edge-Connected Spanning Subgraphs
119
3.4
A Hierarchical Structure of
MA Orderings
123
3.5
Maximum Flows Between a Pendent Pair
127
3.6
A Generalization of Pendent Pairs
130
3.7
Practically Efficient Minimum-Cut Algorithms
131
4
Cut Enumeration
137
4.1
Enumerating All Cuts
137
4.2
Enumerating Small Cuts
140
vii
viii Contents
4.3
Enumerating Minimum Cuts
145
4.4
Upper Bounds on the Number of Small Cuts
149
5
Cactus Representations
153
5.1
Canonical Forms of Cactus Representations
153
5.2
(s, t )-Cactus
Representations
171
5.3
Constructing Cactus Representations
180
6
Extreme Vertex Sets
191
6.1
Computing Extreme Vertex Sets in Graphs
192
6.2
Algorithm for Dynamic Edges Incident to a Specified Vertex
198
6.3
Optimal Contraction Ordering
200
6.4
Minimum ^-Subpartition Problem
207
7
Edge Splitting
217
7.1
Preliminaries
217
7.2
Edge Splitting in Weighted Graphs
220
7.3
Edge Splitting in Multigraphs
226
7.4
Other Splittings
232
7.5
Detachments
237
7.6
Applications of Splittings
240
8
Connectivity Augmentation
246
8.1
Increasing Edge-Connectivity by One
247
8.2
Star Augmentation
249
8.3
Augmenting Multigraphs
252
8.4
Augmenting Weighted Graphs
254
8.5
More on Augmentation
276
9
Source Location Problems
282
9.1
Source Location Problem Under Edge-Connectivity
Requirements
283
9.2
Source Location Problem Under Vertex-Connectivity
Requirements
295
10
Submodular
and Posimodular Set Functions
304
10.1
Set Functions
304
10.2
Minimizing
Submodular
and Posimodular Functions
306
10.3
Extreme Subsets in
Submodular
and Posimodular Systems
315
10.4
Optimization Problems over
Submodular
and Posimodular
Systems
320
10.5
Extreme Points of Base Polyhedron
336
10.6
Minimum Transversal in Set Systems
342
Bibliography
357
Index
371 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T22:14:21Z |
| indexdate | 2024-07-09T21:22:14Z |
| institution | BVB |
| isbn | 9780521878647 |
| language | English |
| lccn | 2008007560 |
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| physical | XV, 375 S. graph. Darst. |
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| series | Encyclopedia of mathematics and its applications |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Nagamochi, Hiroshi Verfasser aut Algorithmic aspects of graph connectivity Hiroshi Nagamochi ; Toshihide Ibaraki 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2008 XV, 375 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 123 Includes index. Graph connectivity Graph algorithms Algorithmische Geometrie (DE-588)4130267-9 gnd rswk-swf Graph (DE-588)4021842-9 gnd rswk-swf Graphentheorie (DE-588)4113782-6 gnd rswk-swf Graph (DE-588)4021842-9 s Algorithmische Geometrie (DE-588)4130267-9 s DE-604 Graphentheorie (DE-588)4113782-6 s 1\p DE-604 Ibaraki, Toshihide Sonstige oth Encyclopedia of mathematics and its applications 123 (DE-604)BV000903719 123 http://www.loc.gov/catdir/enhancements/fy0810/2008007560-b.html Contributor biographical information http://www.loc.gov/catdir/enhancements/fy0810/2008007560-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy0810/2008007560-t.html Table of contents only Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016769497&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Nagamochi, Hiroshi Algorithmic aspects of graph connectivity Encyclopedia of mathematics and its applications Graph connectivity Graph algorithms Algorithmische Geometrie (DE-588)4130267-9 gnd Graph (DE-588)4021842-9 gnd Graphentheorie (DE-588)4113782-6 gnd |
| subject_GND | (DE-588)4130267-9 (DE-588)4021842-9 (DE-588)4113782-6 |
| title | Algorithmic aspects of graph connectivity |
| title_auth | Algorithmic aspects of graph connectivity |
| title_exact_search | Algorithmic aspects of graph connectivity |
| title_exact_search_txtP | Algorithmic aspects of graph connectivity |
| title_full | Algorithmic aspects of graph connectivity Hiroshi Nagamochi ; Toshihide Ibaraki |
| title_fullStr | Algorithmic aspects of graph connectivity Hiroshi Nagamochi ; Toshihide Ibaraki |
| title_full_unstemmed | Algorithmic aspects of graph connectivity Hiroshi Nagamochi ; Toshihide Ibaraki |
| title_short | Algorithmic aspects of graph connectivity |
| title_sort | algorithmic aspects of graph connectivity |
| topic | Graph connectivity Graph algorithms Algorithmische Geometrie (DE-588)4130267-9 gnd Graph (DE-588)4021842-9 gnd Graphentheorie (DE-588)4113782-6 gnd |
| topic_facet | Graph connectivity Graph algorithms Algorithmische Geometrie Graph Graphentheorie |
| url | http://www.loc.gov/catdir/enhancements/fy0810/2008007560-b.html http://www.loc.gov/catdir/enhancements/fy0810/2008007560-d.html http://www.loc.gov/catdir/enhancements/fy0810/2008007560-t.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016769497&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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