Communication complexity:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge ; New York ; Melbourne
Cambridge University Press
2006
|
| Edition: | Digitally printed first paperback version |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xiii, 189 Seiten Illustrationen |
| ISBN: | 9780521029834 052102983X |
Staff View
MARC
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Record in the Search Index
| _version_ | 1808864262826754048 |
|---|---|
| adam_text |
Contents
Preface
χ
I Two-Party Communication Complexity
1
1
Basics
3
1.1
The Model
3
1.2
Rectangles
7
1.3
Fooling Sets and Rectangle Size
10
1.4
Rank Lower Bound
13
1.5
Bibliographic Notes
14
2
More on Covers
16
2.1
Covers and Nondeterminism
16
2.2
Communication Complexity Versus Protocol Cover
19
23
Determinism Versus Nondeterminism
20
2.4
Rectangle Size and Covers
23
2.5
On Rank and Covers
25
2.6
Bibliographic Notes
27
3
Randomization
28
28
31
32
35
38
40
42
42
3.1
Basic Definitions
3.2
Randomization Versus Determinism
33
Public Coin Versus Private Coin
3.4
Distributional Complexity
3.5
Discrepancy
3.6
Bibliographic Notes
4
Advanced Topics
4.1
Direct Sum
CONTENTS
4.1.1
The Randomized Case
44
4.1.2
The Nondeterministic Case
46
4.1.3
The Deterministic Case
47
4.2
Rounds
49
4.3
Asymmetric Communication
54
4.4
Pseudorandomness
57
4.5
Reductions and Complexity Classes
58
4.6
The Disjointness Function
60
4.7
Communication with Partial Information
64
4.8
Bibliographic Notes
67
II Other Models of Communication
69
5
The Communication Complexity of Relations
71
5.1
Basic Examples
74
5.2
The Pair-Disjointness Relation
77
5.3
The fork Relation
79
5.4
Bibliographic Notes
82
6
Multiparty Communication Complexity
83
6.1
The "Number on the Forehead" Model
83
6.2
Cylinder Intersections
85
6.3
Bounds Using Ramsey Theory
87
6.4
Discrepancy Lower Bound
89
6.4.1
The Discrepancy of
GIP
91
6.5
Simultaneous Protocols
92
6.6
Bibliographic Notes
95
7
Variable Partition Models 97
7.1
Worst-Case Partition 97
7.2
Best-Case Partition
99
7.3
Best Partition with Information Overlap
101
7.4
Bibliographic Notes
103
III Applications
105
8
Networks, Communication, and VLSI
107
8.1
Bisection Width of Networks
107
8.2
Total Communication
1
Ю
83
AT2 Lower Bounds for VLSI
П2
8.4
Bibliographic Notes
113
9
Decision Trees and Data Structures
114
9.1
Decision Trees
114
VI
CONTENTS
9.2 Data
Structures
and the Cell
Probe Model 116
9.3
Dynamic Data Structures
117
9.4
Bibliographic Notes
118
10
Boolean Circuit Depth
119
10.1
Introduction
119
10.2
The Connection to Communication Complexity
121
10.3
Matching and Sr-Connectivity
124
10.4
Set Cover
126
10.5
Monotone Constant-Depth Circuits
128
10.6
Bibliographic Notes
129
11
More Boolean Circuit Lower Bounds
131
11.1
Small Circuits
131
11.2
Depth
2
Threshold Circuits
133
11.3
Size-Depth Tradeoffs: An Approach
135
11.4
ACC Circuits
136
11.5
Bibliographic Notes
137
12
Time and Space
139
12.1
Time-Space Tradeoffs for Turing Machines
139
12.2
One-Tape Turing Machines
142
123
Ordered Binary Decision Diagrams (OBDDs)
143
12.4
Width-Length Tradeoff for Branching Programs
145
12.5
Bibliographic Notes
146
13
Randomness
148
13.1
Quasirandom Graphs
148
13.2
Deterministic Amplification
150
13.3
Slightly Random Sources
152
13.4
Bibliographic Notes
154
14
Further Topics
156
156
156
157
158
158
160
162
162
163
166
vü ------
14.1
Noisy Channels
14.2
Communication-Space Tradeoffs
14.3
Privacy
14.4
Algebraic Communication Complexity
14.5
Two-Sided Cards
Index of Notation
A Mathematical Background
A.I
Asymptotics
A.2
Linear Algebra
A3
Probability Theory
CONTENTS
Answers to Selected Problems
168
Bibliography
176
Index
186
viii |
| any_adam_object | 1 |
| author | Kushilevitz, Eyal Nisan, Noam 1961- |
| author_GND | (DE-588)1204492271 (DE-588)137125372 |
| author_facet | Kushilevitz, Eyal Nisan, Noam 1961- |
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| classification_rvk | SK 950 ST 134 |
| classification_tum | DAT 517f |
| ctrlnum | (OCoLC)705505609 (DE-599)BVBBV036453702 |
| discipline | Informatik Mathematik |
| edition | Digitally printed first paperback version |
| format | Book |
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| indexdate | 2024-08-31T01:23:07Z |
| institution | BVB |
| isbn | 9780521029834 052102983X |
| language | English |
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| physical | xiii, 189 Seiten Illustrationen |
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| publisher | Cambridge University Press |
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| spelling | Kushilevitz, Eyal Verfasser (DE-588)1204492271 aut Communication complexity Eyal Kushilevitz, Technion - Israel Institute of Technology, Haifa ; Noam Nisan, Hebrew University, Jerusalem Digitally printed first paperback version Cambridge ; New York ; Melbourne Cambridge University Press 2006 xiii, 189 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Logische Schaltung (DE-588)4131023-8 gnd rswk-swf Komplexitätstheorie (DE-588)4120591-1 gnd rswk-swf Komplexität (DE-588)4135369-9 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Boolesche Algebra (DE-588)4146280-4 gnd rswk-swf Kommunikation (DE-588)4031883-7 gnd rswk-swf Berechnungskomplexität (DE-588)4134751-1 gnd rswk-swf Kommunikation (DE-588)4031883-7 s Komplexitätstheorie (DE-588)4120591-1 s Logische Schaltung (DE-588)4131023-8 s Boolesche Algebra (DE-588)4146280-4 s Berechnungskomplexität (DE-588)4134751-1 s 1\p DE-604 Komplexität (DE-588)4135369-9 s Mathematik (DE-588)4037944-9 s 2\p DE-604 Nisan, Noam 1961- Verfasser (DE-588)137125372 aut Äquivalent Druck-Ausgabe, Hardcover 978-0-521-56067-2 Äquivalent Druck-Ausgabe, Hardcover 0-521-56067-5 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020325758&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 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kushilevitz, Eyal Nisan, Noam 1961- Communication complexity Logische Schaltung (DE-588)4131023-8 gnd Komplexitätstheorie (DE-588)4120591-1 gnd Komplexität (DE-588)4135369-9 gnd Mathematik (DE-588)4037944-9 gnd Boolesche Algebra (DE-588)4146280-4 gnd Kommunikation (DE-588)4031883-7 gnd Berechnungskomplexität (DE-588)4134751-1 gnd |
| subject_GND | (DE-588)4131023-8 (DE-588)4120591-1 (DE-588)4135369-9 (DE-588)4037944-9 (DE-588)4146280-4 (DE-588)4031883-7 (DE-588)4134751-1 |
| title | Communication complexity |
| title_auth | Communication complexity |
| title_exact_search | Communication complexity |
| title_full | Communication complexity Eyal Kushilevitz, Technion - Israel Institute of Technology, Haifa ; Noam Nisan, Hebrew University, Jerusalem |
| title_fullStr | Communication complexity Eyal Kushilevitz, Technion - Israel Institute of Technology, Haifa ; Noam Nisan, Hebrew University, Jerusalem |
| title_full_unstemmed | Communication complexity Eyal Kushilevitz, Technion - Israel Institute of Technology, Haifa ; Noam Nisan, Hebrew University, Jerusalem |
| title_short | Communication complexity |
| title_sort | communication complexity |
| topic | Logische Schaltung (DE-588)4131023-8 gnd Komplexitätstheorie (DE-588)4120591-1 gnd Komplexität (DE-588)4135369-9 gnd Mathematik (DE-588)4037944-9 gnd Boolesche Algebra (DE-588)4146280-4 gnd Kommunikation (DE-588)4031883-7 gnd Berechnungskomplexität (DE-588)4134751-1 gnd |
| topic_facet | Logische Schaltung Komplexitätstheorie Komplexität Mathematik Boolesche Algebra Kommunikation Berechnungskomplexität |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020325758&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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