Global methods for combinatorial isoperimetric problems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2004
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| Schriftenreihe: | Cambridge studies in advanced mathematics
90 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 232 S. graph. Darst. |
| ISBN: | 0521832683 |
Internformat
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| 245 | 1 | 0 | |a Global methods for combinatorial isoperimetric problems |c L. H. Harper |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface page ix
1 The edge-isoperimetric problem 1
1.1 Basic definitions 1
1.2 Examples 1
1.3 Application to layout problems 9
1.4 Comments 18
2 The minimum path problem 20
2.1 Introduction 20
2.2 Algorithms 21
2.3 Reduction of wirelength to minpath 24
2.4 Pathmorphisms 25
2.5 Comments 29
3 Stabilization and compression 32
3.1 Introduction 32
3.2 Stabilization 32
3.3 Compression 44
3.4 Comments 49
4 The vertex-isoperimetric problem 52
4.1 Definitions and examples 52
4.2 Stabilization and VIP 53
4.3 Compression for VIP 56
4.4 Optimality of Hales numbering 59
4.5 Applications to layout problems 61
4.6 Comments 66
5 Stronger stabilization 68
5.1 Graphs of regular solids 68
5.2 A summary of Coxeter theory 74
vii
viii Contents
5.3 The structure of stability orders 79
5.4 Calculating stability orders 82
5.5 Into the fourth dimension 85
5.6 Extended stabilization 96
5.7 Comments 100
6 Higher compression 103
6.1 Additivity 103
6.2 The MWI problem 107
6.3 The Ahlswede-Cai theorem 109
6.4 The Bezrukov-Das-Elsasser theorem 115
6.5 Comments 125
7 Isoperimetric problems on infinite graphs 128
7.1 Euclidean tessellations 129
7.2 Comments 142
8 Isoperimetric problems on complexes 145
8.1 Minimum shadow problems 146
8.2 Steiner operations for MSP 152
8.3 Scheduling problems 162
8.4 Comments 166
9 Morphisms for MWI problems 169
9.1 MWI-morphisms 169
9.2 Examples 173
9.3 Application I: The pairwise product of Petersen graphs 180
9.4 Application II: The EIP on the 600-vertex 182
9.5 The calculation for V600 185
9.6 Comments 194
10 Passage to the limit 196
10.1 The Bollobas-Leader theorem 196
10.2 The Kleitman-West problem 202
10.3 VIP on the Hamming graph 208
10.4 Sapozhenko s problem 209
10.5 Comments 213
Afterword 217
Appendix: The classical isoperimetric problem 219
References 223
Index 229
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV023843321 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:37:50Z |
| institution | BVB |
| isbn | 0521832683 |
| language | English |
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| physical | XIV, 232 S. graph. Darst. |
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| publisher | Cambridge Univ. Press |
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| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Harper, Lawrence H. Verfasser aut Global methods for combinatorial isoperimetric problems L. H. Harper Cambridge [u.a.] Cambridge Univ. Press 2004 XIV, 232 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge studies in advanced mathematics 90 Kombinatorische Optimierung (DE-588)4031826-6 gnd rswk-swf Kombinatorische Optimierung (DE-588)4031826-6 s DE-604 Cambridge studies in advanced mathematics 90 (DE-604)BV000003678 90 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017485361&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Harper, Lawrence H. Global methods for combinatorial isoperimetric problems Cambridge studies in advanced mathematics Kombinatorische Optimierung (DE-588)4031826-6 gnd |
| subject_GND | (DE-588)4031826-6 |
| title | Global methods for combinatorial isoperimetric problems |
| title_auth | Global methods for combinatorial isoperimetric problems |
| title_exact_search | Global methods for combinatorial isoperimetric problems |
| title_full | Global methods for combinatorial isoperimetric problems L. H. Harper |
| title_fullStr | Global methods for combinatorial isoperimetric problems L. H. Harper |
| title_full_unstemmed | Global methods for combinatorial isoperimetric problems L. H. Harper |
| title_short | Global methods for combinatorial isoperimetric problems |
| title_sort | global methods for combinatorial isoperimetric problems |
| topic | Kombinatorische Optimierung (DE-588)4031826-6 gnd |
| topic_facet | Kombinatorische Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017485361&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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