Counting, sampling and integrating: algorithms and complexity:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
2003
|
| Series: | Lectures in mathematics : ETH Zürich
|
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010211529&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Item Description: | Literaturverz. S. 105 - 110 |
| Physical Description: | XI, 112 Seiten Diagramme |
| ISBN: | 3764369469 |
Staff View
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Record in the Search Index
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Titel: Counting, sampling and integrating: algorithms and complexity
Autor: Jerrum, Mark
Jahr: 2003
Contents
Foreword ix
1 Two good counting algorithms 1
1.1 Spanning trees. 1
1.2 Perfect matchings in a planar graph. 5
2 #P-completeness 11
2.1 The class #P. 13
2.2 A primal #P-complete problem. 15
2.3 Computing the permanent is hard on average. 21
3 Sampling and counting 25
3.1 Preliminaries. 25
3.2 Reducing approximate counting
to almost uniform sampling. 28
3.3 Markov chains . 30
4 Coupling and colourings 33
4.1 Colourings of a low-degree graph. 33
4.2 Bounding mixing time using coupling. 36
4.3 Path coupling. 41
5 Canonical paths and matchings 49
5.1 Matchings in a graph. 49
5.2 Canonical paths. 51
5.3 Back to matchings. 56
5.4 Extensions and further applications. 62
5.5 Continuous time. 63
6 Volume of a convex body 65
6.1 A few remarks on Markov chains
with continuous state space. 67
6.2 Invariant measure of the ball walk . 68
viii Contents
6.3 Mixing rate of the ball walk. 72
6.4 Proof of the Poincaré inequality (Theorem 6.7). 74
6.5 Proofs of the geometric lemmas. 82
6.6 Relaxing the curvature condition. 85
6.7 Using samples to estimate volume . 89
6.8 Appendix: a proof of Corollary 6.8. 91
7 Inapproximability 93
7.1 Independent sets in a low degree graph. 96
Bibliography 105 |
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| author | Jerrum, Mark 1955- |
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| dewey-full | 511/.62 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
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| illustrated | Not Illustrated |
| indexdate | 2025-01-11T15:52:01Z |
| institution | BVB |
| isbn | 3764369469 |
| language | English |
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| physical | XI, 112 Seiten Diagramme |
| publishDate | 2003 |
| publishDateSearch | 2003 |
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| publisher | Birkhäuser |
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| series2 | Lectures in mathematics : ETH Zürich |
| spelling | Jerrum, Mark 1955- Verfasser (DE-588)12443133X aut Counting, sampling and integrating: algorithms and complexity Mark Jerrum Basel [u.a.] Birkhäuser 2003 XI, 112 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Lectures in mathematics : ETH Zürich Literaturverz. S. 105 - 110 Algorithmes Algoritmen gtt Complexiteit gtt Complexité de calcul (Informatique) Problèmes combinatoires d'énumération Algorithms Combinatorial enumeration problems Computational complexity Markov-Prozess (DE-588)4134948-9 gnd rswk-swf Graph (DE-588)4021842-9 gnd rswk-swf Markov-Ketten-Monte-Carlo-Verfahren (DE-588)4508520-1 gnd rswk-swf Berechnungskomplexität (DE-588)4134751-1 gnd rswk-swf Graph (DE-588)4021842-9 s Markov-Prozess (DE-588)4134948-9 s Berechnungskomplexität (DE-588)4134751-1 s DE-604 Markov-Ketten-Monte-Carlo-Verfahren (DE-588)4508520-1 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010211529&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jerrum, Mark 1955- Counting, sampling and integrating: algorithms and complexity Algorithmes Algoritmen gtt Complexiteit gtt Complexité de calcul (Informatique) Problèmes combinatoires d'énumération Algorithms Combinatorial enumeration problems Computational complexity Markov-Prozess (DE-588)4134948-9 gnd Graph (DE-588)4021842-9 gnd Markov-Ketten-Monte-Carlo-Verfahren (DE-588)4508520-1 gnd Berechnungskomplexität (DE-588)4134751-1 gnd |
| subject_GND | (DE-588)4134948-9 (DE-588)4021842-9 (DE-588)4508520-1 (DE-588)4134751-1 |
| title | Counting, sampling and integrating: algorithms and complexity |
| title_auth | Counting, sampling and integrating: algorithms and complexity |
| title_exact_search | Counting, sampling and integrating: algorithms and complexity |
| title_full | Counting, sampling and integrating: algorithms and complexity Mark Jerrum |
| title_fullStr | Counting, sampling and integrating: algorithms and complexity Mark Jerrum |
| title_full_unstemmed | Counting, sampling and integrating: algorithms and complexity Mark Jerrum |
| title_short | Counting, sampling and integrating: algorithms and complexity |
| title_sort | counting sampling and integrating algorithms and complexity |
| topic | Algorithmes Algoritmen gtt Complexiteit gtt Complexité de calcul (Informatique) Problèmes combinatoires d'énumération Algorithms Combinatorial enumeration problems Computational complexity Markov-Prozess (DE-588)4134948-9 gnd Graph (DE-588)4021842-9 gnd Markov-Ketten-Monte-Carlo-Verfahren (DE-588)4508520-1 gnd Berechnungskomplexität (DE-588)4134751-1 gnd |
| topic_facet | Algorithmes Algoritmen Complexiteit Complexité de calcul (Informatique) Problèmes combinatoires d'énumération Algorithms Combinatorial enumeration problems Computational complexity Markov-Prozess Graph Markov-Ketten-Monte-Carlo-Verfahren Berechnungskomplexität |
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