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Combinatorial group testing and its applications

Author: Dingzhu Du; Frank Hwang
Publisher: Singapore ; River Edge, N.J. : World Scientific, ©1993.
Series: Series on applied mathematics, v. 3.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
Group testing was first proposed for blood tests, but soon found its way to many industrial applications. Combinatorial group testing studies the combinatorial aspect of the problem and is particularly related to many topics in combinatorics, computer science and operations research. Recently, the idea of combinatorial group testing has been applied to experimental designs, coding, multiaccess computer  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Du, Dingzhu.
Combinatorial group testing and its applications.
Singapore ; River Edge, N.J. : World Scientific, ©1993
(DLC) 93026812
(OCoLC)28506287
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Dingzhu Du; Frank Hwang
ISBN: 9789812798183 9812798188
OCLC Number: 829714039
Description: 1 online resource (x, 249 pages) : illustrations.
Contents: Ch. 1. Introduction. 1.1. The History of Group Testing. 1.2. The Binary Tree Representation of a Group Testing Algorithm and the Information Lower Bound. 1.3. The Structure of Group Testing. 1.4. Number of Group Testing Algorithms. 1.5. A Prototype Problem and Some Basic Inequalities. 1.6. Variations of the Prototype Problem --
Ch. 2. General Algorithms. 2.1. Li's s-Stage Algorithm. 2.2. Hwang's Generalized Binary Splitting Algorithm. 2.3. The Nested Class. 2.4. (d, n) Algorithms and Merging Algorithms. 2.5. Some Practical Considerations. 2.6. An Application to Clone Screenings --
Ch. 3. Algorithms for Special Cases. 3.1. Two Disjoint Sets Each Containing Exactly One Defective. 3.2. An Application to Locating Electrical Shorts. 3.3. The 2-Defective Case. 3.4. The 3-Defective Case. 3.5. When is Individual Testing Minimax? 3.6. Identifying a Single Defective with Parallel Tests --
Ch. 4. Nonadaptive Algorithms and Binary Superimposed Codes. 4.1. The Matrix Representation. 4.2. Basic Relations and Bounds. 4.3. Constant Weight Matrices and Random Codes. 4.4. General Constructions. 4.5. Special Constructions --
Ch. 5. Multiaccess Channels and Extensions. 5.1. Multiaccess Channels. 5.2. Nonadaptive Algorithms. 5.3. Two Variations. 5.4. The k-Channel. 5.5. Quantitative Channels --
Ch. 6. Some Other Group Testing Models. 6.1. Symmetric Group Testing. 6.2. Some Additive Models. 6.3. A Maximum Model. 6.4. Some Models for d = 2 --
Ch. 7. Competitive Group Testing. 7.1. The First Competitiveness. 7.2. Bisecting. 7.3. Doubling. 7.4. Jumping. 7.5. The Second Competitiveness. 7.6. Digging. 7.7. Tight Bound --
Ch. 8. Unreliable Tests. 8.1. Ulam's Problem. 8.2. General Lower and Upper Bounds. 8.3. Linearly Bounded Lies (1). 8.4. The Chip Game. 8.5. Linearly Bounded Lies (2). 8.6. Other Restrictions on Lies --
Ch. 9. Optimal Search in One Variable. 9.1. Midpoint Strategy. 9.2. Fibonacci Search. 9.3. Minimum Root Identification --
Ch. 10. Unbounded Search. 10.1. Introduction. 10.2. Bentley-Yao Algorithms. 10.3. Search with Lies. 10.4. Unbounded Fibonacci Search --
Ch. 11. Group Testing on Graphs. 11.1. On Bipartite Graphs. 11.2. On Graphs. 11.3. On Hypergraphs. 11.4. On Trees. 11.5. Other Constraints --
Ch. 12. Membership Problems. 12.1. Examples. 12.2. Polyhedral Membership. 12.3. Boolean Formulas and Decision Trees. 12.4. Recognition of Graph Properties --
Ch. 13. Complexity Issues. 13.1. General Notions. 13.2. The Prototype Problem is in PSPACE. 13.3. Consistency. 13.4. Determinacy. 13.5. On Sample Space S(n). 13.6. Learning by Examples.
Series Title: Series on applied mathematics, v. 3.
Responsibility: Ding-Zhu Du, Frank K. Hwang.
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Abstract:

Group testing was first proposed for blood tests, but soon found its way to many industrial applications. This text attempts to cover both the theory and applications of combinatorial group testing  Read more...

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