Design of survivable networks:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1992
|
| Series: | Lecture notes in mathematics
1531 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 204 S. graph. Darst. |
| ISBN: | 3540562710 0387562710 9783540562719 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | Contents
1 Motivation 5
2 Network Survivability Models Using Node Types 7
2.1 Survivable Telephone Networks 7
2.2 Graph theoretic Formulation 9
2.3 Integer LP Formulation and Associated Polyhedra 14
2.4 An Outline of the Cutting Plane Procedure 16
2.5 Outlook on the Contents 17
3 Survivable Network Design under Connectivity Constraints —
a Survey 19
3.1 Polynomially Solvable Cases 21
3.2 Results for Restricted Costs 25
3.3 Heuristics for General Costs 27
3.4 Exact Algorithms for General Costs 30
4 Decomposition 33
4.1 Bridges, Articulation Nodes, and Paths 34
4.2 Articulation Sets of Size 2 for 2NCON 34
4.3 Articulation Sets of Size 2 for 1ECON 36
4.4 Cutsets of Size 3 for 2CON 40
4.5 Cutsets of Size Jb for fcCON 44
5 Basic Inequalities 49
5.1 Dimension and Trivial Inequalities 49
5.2 Cut Constraints for Low Connectivity 51
5.3 Cut Constraints for fcECON 55
5.4 Node Cut Constraints for 2NCON 63
5.5 (Node) Cut Constraints for ArNCON 66
6 Lifting Theorems 69
6.1 Expansion of Nodes 70
6.2 Addition of Edges 73
6.3 Addition of Nodes of Type 1 74
2 CONTENTS
7 Partition Inequalities 77
7.1 Motivation 77
7.2 Facet Results for fcECON 79
7.3 Facet Results for ifcNCON 85
7.4 Facet Results for Low Connectivity 88
8 Node Partition Inequalities 91
8.1 Generalization of Node Cut Constraints 91
8.2 Validity 93
8.3 Facet Results 94
9 Lifted r Cover Inequalities 101
9.1 Motivation 101
9.2 r Cover Inequalities 103
9.3 Lifted r Cover Inequalities 109
10 Comb Inequalities 113
10.1 Comb Inequalities for 2NCON 113
10.2 Comb Inequalities for ifcNCON 117
10.3 Comb Inequalities for 2ECON 119
11 How to Find Valid Inequalities 125
11.1 Related Polyhedra 126
11.1.1 Special Cases 126
11.1.2 Relaxation 127
11.1.3 Subfaces 128
11.1.4 Projection and Prodon Inequalities 130
11.2 Small Polyhedra 134
11.3 Generalization of Validity Proofs 142
11.4 Fractional Solutions 146
11.5 Redundant Inequalities • 150
11.5.1 Little Man Inequalities 152
11.6 Open Problems 153
12 Implementation of the Cutting Plane Algorithm 155
12.1 The Framework 155
12.2 Complexity of the Separation Problems • 157
12.3 Separating Partition Inequalities 161
12.3.1 Transforming Cuts into Partitions 162
12.3.2 Shrinking Criteria for Partition Inequalities 165
12.4 Separating Node Partition Inequalities • 166
12.5 Separating Lifted r Cover Inequalities 168
12.5.1 Shrinking One Paths • 170
12.5.2 The Padberg Rao Algorithm • 170
12.5.3 Converting H, T into a Lifted r Cover Constraint • 172
12.6 Other Details • 172
CONTENTS 3
13 Computational Results 175
13.1 Low Connectivity Problems 175
13.2 High Connectivity Problems 183
13.2.1 Random Problems 183
13.2.2 The Ship Problem 187
Conclusion 195
Bibliography 197
Index 205
|
| any_adam_object | 1 |
| author | Stoer, Mechthild |
| author_facet | Stoer, Mechthild |
| author_role | aut |
| author_sort | Stoer, Mechthild |
| author_variant | m s ms |
| building | Verbundindex |
| bvnumber | BV005863961 |
| classification_rvk | SI 850 SK 890 |
| classification_tum | DAT 195f MAT 059f |
| ctrlnum | (OCoLC)231402804 (DE-599)BVBBV005863961 |
| discipline | Informatik Mathematik |
| format | Thesis Book |
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| id | DE-604.BV005863961 |
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| indexdate | 2024-07-09T16:35:59Z |
| institution | BVB |
| isbn | 3540562710 0387562710 9783540562719 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003672484 |
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| physical | 204 S. graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
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| publisher | Springer |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Stoer, Mechthild Verfasser aut Design of survivable networks Mechthild Stoer Berlin [u.a.] Springer 1992 204 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1531 Zugl.: Augsburg, Univ., Diss., 1991 Graphentheorie (DE-588)4113782-6 gnd rswk-swf Robustheit (DE-588)4126481-2 gnd rswk-swf Kostenoptimierung (DE-588)4135132-0 gnd rswk-swf Netzwerktopologie (DE-588)4208537-8 gnd rswk-swf Netzwerktheorie (DE-588)4171531-7 gnd rswk-swf Polyedrische Kombinatorik (DE-588)4132100-5 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf Redundanz (DE-588)4157937-9 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Netzwerktopologie (DE-588)4208537-8 s Redundanz (DE-588)4157937-9 s Kostenoptimierung (DE-588)4135132-0 s DE-604 Algorithmus (DE-588)4001183-5 s Polyedrische Kombinatorik (DE-588)4132100-5 s Netzwerktheorie (DE-588)4171531-7 s Robustheit (DE-588)4126481-2 s Graphentheorie (DE-588)4113782-6 s Lecture notes in mathematics 1531 (DE-604)BV000676446 1531 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003672484&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stoer, Mechthild Design of survivable networks Lecture notes in mathematics Graphentheorie (DE-588)4113782-6 gnd Robustheit (DE-588)4126481-2 gnd Kostenoptimierung (DE-588)4135132-0 gnd Netzwerktopologie (DE-588)4208537-8 gnd Netzwerktheorie (DE-588)4171531-7 gnd Polyedrische Kombinatorik (DE-588)4132100-5 gnd Algorithmus (DE-588)4001183-5 gnd Redundanz (DE-588)4157937-9 gnd |
| subject_GND | (DE-588)4113782-6 (DE-588)4126481-2 (DE-588)4135132-0 (DE-588)4208537-8 (DE-588)4171531-7 (DE-588)4132100-5 (DE-588)4001183-5 (DE-588)4157937-9 (DE-588)4113937-9 |
| title | Design of survivable networks |
| title_auth | Design of survivable networks |
| title_exact_search | Design of survivable networks |
| title_full | Design of survivable networks Mechthild Stoer |
| title_fullStr | Design of survivable networks Mechthild Stoer |
| title_full_unstemmed | Design of survivable networks Mechthild Stoer |
| title_short | Design of survivable networks |
| title_sort | design of survivable networks |
| topic | Graphentheorie (DE-588)4113782-6 gnd Robustheit (DE-588)4126481-2 gnd Kostenoptimierung (DE-588)4135132-0 gnd Netzwerktopologie (DE-588)4208537-8 gnd Netzwerktheorie (DE-588)4171531-7 gnd Polyedrische Kombinatorik (DE-588)4132100-5 gnd Algorithmus (DE-588)4001183-5 gnd Redundanz (DE-588)4157937-9 gnd |
| topic_facet | Graphentheorie Robustheit Kostenoptimierung Netzwerktopologie Netzwerktheorie Polyedrische Kombinatorik Algorithmus Redundanz Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003672484&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT stoermechthild designofsurvivablenetworks |