NDLI: Optimal Two-Stage Algorithms for Group Testing Problems

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Gasieniec, Leszek Vaccaro, Ugo De Bonis, Annalisa
Copyright Year	2005
Abstract	Group testing refers to the situation in which one is given a set of objects ${\cal O}$, an unknown subset ${\cal P}\subseteq {\cal O}$, and the task of determining ${\cal P}$ by asking queries of the type "does ${\cal P}$ intersect $\cal Q$?," where $\cal Q$ is a subset of ${\cal O}$. Group testing is a basic search paradigm that occurs in a variety of situations such as quality control testing, searching in storage systems, multiple access communications, and data compression, among others. Group testing procedures have been recently applied in computational molecular biology, where they are used for screening libraries of clones with hybridization probes and sequencing by hybridization.Motivated by particular features of group testing algorithms used in biological screening, we study the efficiency of two-stage group testing procedures. Our main result is the first optimal two-stage algorithm that uses a number of tests of the same order as the information-theoretic lower bound on the problem. We also provide efficient algorithms for the case in which there is a Bernoulli probability distribution on the possible sets ${\cal P}$, and an optimal algorithm for the case in which the outcome of tests may be unreliable because of the presence of "inhibitory" items in ${\cal O}$. Our results depend on a combinatorial structure introduced in this paper. We believe that it will prove useful in other contexts, too.
Starting Page	1253
Ending Page	1270
Page Count	18
File Format	PDF
ISSN	00975397
DOI	10.1137/S0097539703428002
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	5
Volume Number	34
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-27
Access Restriction	Subscribed
Subject Keyword	cover-free families Analysis of algorithms and problem complexity group testing Searching and sorting Combinatorics Extremal set theory
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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