TY - JOUR
T1 - Optimal two-stage algorithms for group testing problems
AU - De Bonis, Annalisa
AU - Ga̧sieniec, Leszek
AU - Vaccaro, Ugo
N1 - Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.
PY - 2005
Y1 - 2005
N2 - Group testing refers to the situation in which one is given a set of objects script O sign, an unknown subset P ⊆ script O sign, and the task of determining P by asking queries of the type "does P intersect Q?", where Q is a subset of script O sign. 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 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 script O sign. Our results depend on a combinatorial structure introduced in this paper. We believe that it will prove useful in other contexts, too.
AB - Group testing refers to the situation in which one is given a set of objects script O sign, an unknown subset P ⊆ script O sign, and the task of determining P by asking queries of the type "does P intersect Q?", where Q is a subset of script O sign. 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 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 script O sign. Our results depend on a combinatorial structure introduced in this paper. We believe that it will prove useful in other contexts, too.
KW - Cover-free families
KW - Group testing
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U2 - 10.1137/S0097539703428002
DO - 10.1137/S0097539703428002
M3 - Article
AN - SCOPUS:27144547067
VL - 34
SP - 1253
EP - 1270
JO - SIAM Journal on Computing
JF - SIAM Journal on Computing
SN - 0097-5397
IS - 5
ER -