Combinatorial group testing and its applications

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Combinatorial group testing and its applications / Ding-Zhu Du, Frank K. Hwang

版:

2nd ed.

資料種別:

図書

出版情報:

Singapore ; New Jersey : World Scientific, c2000

形態:

xii, 323 p. ; 23 cm

シリーズ名:

Series on applied mathematics ; v. 12 <BA19087879>

著者名:

ISBN:

9789810241070 [9810241070]

書誌ID:

BA46123217

子書誌情報

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書誌詳細

注記:

Includes bibliographical references and index

主題:

Combinatorial group theory

言語:

英語

目次情報:

Preface

Preface to the Second Edition

Introduction / Chapter 1：

The History of Group Testing / 1.1：

A Prototype Problem and Some General Remarks / 1.2：

Some Practical Considerations / 1.3：

References

Sequential Group Testing Algorithms / Part I：

General Sequential Algorithms / Chapter 2：

The Binary Tree Representation of a Sequential Algorithm / 2.1：

The Structure of Group Testing / 2.2：

Li's s-Stage Algorithm / 2.3：

Hwang's Generalized Binary Splitting Algorithm / 2.4：

The Nested Class / 2.5：

(d, n) Algorithms and Merging Algorithms / 2.6：

Number of Group Testing Algorithms / 2.7：

Sequential Algorithms for Special Cases / Chapter 3：

Two Disjoint Sets Each Containing Exactly One Defective / 3.1：

An Application to Locating Electrical Shorts / 3.2：

The 2-Defective Case / 3.3：

The 3-Defective Case / 3.4：

When is Individual Testing Minimax? / 3.5：

Identifying a Single Defective with Parallel Tests / 3.6：

Competitive Group Testing / Chapter 4：

The First Competitiveness / 4.1：

Bisecting / 4.2：

Doubling / 4.3：

Jumping / 4.4：

The Second Competitiveness / 4.5：

Digging / 4.6：

Tight Bound / 4.7：

Unreliable Tests / Chapter 5：

Ulam's Problem / 5.1：

General Lower and Upper Bounds / 5.2：

Linearly Bounded Lies (1) / 5.3：

The Chip Game / 5.4：

Linearly Bounded Lies (2) / 5.5：

Other Restrictions on Lies / 5.6：

Complexity Issues / Chapter 6：

General Notions / 6.1：

The Prototype Group Testing Problem is in PSPACE / 6.2：

Consistency / 6.3：

Determinacy / 6.4：

On Sample Space S(n) / 6.5：

Learning by Examples / 6.6：

Nonadaptive Group Testing Algorithms / Part II.：

Deterministic Designs and Superimposed Codes / Chapter 7：

The Matrix Representation / 7.1：

Basic Relations and Bounds / 7.2：

Constant Weight Matrices / 7.3：

General Constructions / 7.4：

The Small d Cases / 7.5：

Random Designs and Error Tolerance / Chapter 8：

Random Matrices / 8.1：

Macula's Error Tolerance d-Disjunct Matrices / 8.2：

q-Error-Tolerance d-Disjunct Matrices / 8.3：

DNA Applications / Chapter 9：

Clone Library Screening / 9.1：

Deterministic Designs / 9.2：

Random Designs / 9.3：

Some Additional Problems / 9.4：

Extended Group Testing Models / Part III.：

Multiaccess Channels and Extensions / Chapter 10：

Multiaccess Channels / 10.1：

Nonadaptive Algorithms / 10.2：

Two Variations / 10.3：

The k-Channel / 10.4：

Quantitative Channels / 10.5：

Additive Model and Others / Chapter 11：

Symmetric Group Testing / 11.1：

Some Additive Models / 11.2：

A Maximum Model / 11.3：

Some Models for d = 2 / 11.4：

Group Testing on Graphs / Chapter 12：

2-Optimal Graphs / 12.1：

Solution of the Du-Hwang Conjecture / 12.2：

Defective Vertices / 12.3：

On Trees / 12.4：

Other Constraints / 12.5：

Other Related Searching Problems / Part IV.：

Optimal Search in One Variable / Chapter 13：

Midpoint Strategy / 13.1：

Fibonacci Search / 13.2：

Minimum Root Identification / 13.3：

Unbounded Search / Chapter 14：

Bentley-Yao Algorithms / 14.1：

Search with Lies / 14.3：

Unbounded Fibonacci Search / 14.4：

Membership Problems / Chapter 15：

Examples / 15.1：

Polyhedral Membership / 15.2：

Boolean Formulas and Decision Trees / 15.3：

Recognition of Graph Properties / 15.4：

Counterfeit Coins / Chapter 16：

One Counterfeit Coin / 16.1：

Two, Three, and More Counterfeit Coins / 16.2：

The All-Equal Problem / 16.3：

Anti-Hadamard Matrices / 16.4：

Coins with Arbitrary Weights / 16.5：

Index

Preface

Preface to the Second Edition

Introduction / Chapter 1：

The History of Group Testing / 1.1：

A Prototype Problem and Some General Remarks / 1.2：

Some Practical Considerations / 1.3：

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