Combinatorial group testing and its applications:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore u.a.
World Scientific
1993
|
| Series: | Series on applied mathematics
3 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 249 S. graph. Darst. |
| ISBN: | 9810212933 |
Staff View
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| 245 | 1 | 0 | |a Combinatorial group testing and its applications |c Ding-Zhu Du ; Frank K. Hwang |
| 264 | 1 | |a Singapore u.a. |b World Scientific |c 1993 | |
| 300 | |a X, 249 S. |b graph. Darst. | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface v
Chapter 1 Introduction 1
1.1 The History of Group Testing 1
1.2 The Binary Tree Representation of a Group Testing Algorithm
and the Information Lower Bound 5
1.3 The Structure of Group Testing 7
1.4 Number of Group Testing Algorithms 10
1.5 A Prototype Problem and Some Basic Inequalities 12
1.6 Variations of the Prototype Problem 17
References 18
Chapter 2 General Algorithms 19
2.1 Li s s Stage Algorithm 19
2.2 Hwang s Generalized Binary Splitting Algorithm 20
2.3 The Nested Class 23
2.4 (d, n) Algorithms and Merging Algorithms 27
2.5 Some Practical Considerations 30
2.6 An Application to Clone Screenings 34
References 36
Chapter 3 Algorithms for Special Cases 38
3.1 Two Disjoint Sets Each Containing Exactly One Defective 38
3.2 An Application to Locating Electrical Shorts 43
3.3 The 2 Defective Case 48
3.4 The 3 Defective Case 53
3.5 When is Individual Testing Minimax? 56
3.6 Identifying a Single Defective with Parallel Tests 59
References 60
vii
viii Contents
Chapter 4 Nonadaptive Algorithms and Binary Superimposed Codes . 62
4.1 The Matrix Representation 62
4.2 Basic Relations and Bounds 63
4.3 Constant Weight Matrices and Random Codes 68
4.4 General Constructions 73
4.5 Special Constructions 78
References 87
Chapter 5 Multiaccess Channels and Extensions 91
5.1 Multiaccess Channels 92
5.2 Nonadaptive Algorithms 96
5.3 Two Variations 99
5.4 The k Channel 101
5.5 Quantitative Channels 105
References 105
Chapter 6 Some Other Group Testing Models 107
6.1 Symmetric Group Testing 107
6.2 Some Additive Models 109
6.3 A Maximum Model 115
6.4 Some Models for d = 2 118
References 123
Chapter 7 Competitive Group Testing 126
7.1 The First Competitiveness 126
7.2 Bisecting 128
7.3 Doubling 132
7.4 Jumping 134
7.5 The Second Competitiveness 138
7.6 Digging ; 140
7.7 Tight Bound 143
References 148
Chapter 8 Unreliable Tests 149
8.1 Ulam s Problem 149
8.2 General Lower and Upper Bounds 155
8.3 Linearly Bounded Lies (1) 160
Contents ;x
8.4 The Chip Game 164
8.5 Linearly Bounded Lies (2) 168
8.6 Other Restrictions on Lies 172
References 175
Chapter 9 Optimal Search in One Variable 177
9.1 Midpoint Strategy 177
9.2 Fibonacci Search 179
9.3 Minimum Root Identification 183
References 190
Chapter 10 Unbounded Search 193
10.1 Introduction 193
10.2 Bentley Yao Algorithms 195
10.3 Search with Lies 199
10.4 Unbounded Fibonacci Search 200
References 202
Chapter 11 Group Testing on Graphs 203
11.1 On Bipartite Graphs 203
11.2 On Graphs 205
11.3 On Hypergraphs 207
11.4 On Trees 212
11.5 Other Constraints 216
References 217
Chapter 12 Membership Problems 218
12.1 Examples 218
12.2 Polyhedral Membership 220
12.3 Boolean Formulas and Decision Trees 222
12.4 Recognition of Graph Properties 226
References 229
Chapter 13 Complexity Issues 231
13.1 General Notions 231
13.2 The Prototype Problem is in PSPACE 233
I
x Contents
13.3 Consistency 234
13.4 Determinacy 236
13.5 On Sample Space S(n) 237
13.6 Learning by Examples 243
References 244
Index 245
|
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| dewey-raw | 512/.2 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV009775263 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:40:40Z |
| institution | BVB |
| isbn | 9810212933 |
| language | English |
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| physical | X, 249 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | World Scientific |
| record_format | marc |
| series | Series on applied mathematics |
| series2 | Series on applied mathematics |
| spelling | Du, Dingzhu 1948- Verfasser (DE-588)1013682580 aut Combinatorial group testing and its applications Ding-Zhu Du ; Frank K. Hwang Singapore u.a. World Scientific 1993 X, 249 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Series on applied mathematics 3 Combinatorial group theory Kombinatorische Gruppentheorie (DE-588)4219556-1 gnd rswk-swf Statistischer Test (DE-588)4077852-6 gnd rswk-swf Kombinatorische Gruppentheorie (DE-588)4219556-1 s DE-604 Statistischer Test (DE-588)4077852-6 s DE-188 Hwang, Frank K. Verfasser aut Series on applied mathematics 3 (DE-604)BV007228284 3 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006467644&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Du, Dingzhu 1948- Hwang, Frank K. Combinatorial group testing and its applications Series on applied mathematics Combinatorial group theory Kombinatorische Gruppentheorie (DE-588)4219556-1 gnd Statistischer Test (DE-588)4077852-6 gnd |
| subject_GND | (DE-588)4219556-1 (DE-588)4077852-6 |
| title | Combinatorial group testing and its applications |
| title_auth | Combinatorial group testing and its applications |
| title_exact_search | Combinatorial group testing and its applications |
| title_full | Combinatorial group testing and its applications Ding-Zhu Du ; Frank K. Hwang |
| title_fullStr | Combinatorial group testing and its applications Ding-Zhu Du ; Frank K. Hwang |
| title_full_unstemmed | Combinatorial group testing and its applications Ding-Zhu Du ; Frank K. Hwang |
| title_short | Combinatorial group testing and its applications |
| title_sort | combinatorial group testing and its applications |
| topic | Combinatorial group theory Kombinatorische Gruppentheorie (DE-588)4219556-1 gnd Statistischer Test (DE-588)4077852-6 gnd |
| topic_facet | Combinatorial group theory Kombinatorische Gruppentheorie Statistischer Test |
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