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Generalized Framework for Selectors with Applications in Optimal Group Testing

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Automata, Languages and Programming (ICALP 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2719))

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Abstract

Group Testing refers to the situation in which one is given a set of objects \( \mathcal{O} \), an unknown subset \( \mathcal{P} \subseteq \mathcal{O} \), and the task is to determine \( \mathcal{P} \) by asking queries of the type “does \( \mathcal{P} \) intersect \( \mathcal{Q} \)?”, where \( \mathcal{Q} \) is a subset of \( \mathcal{O} \). Group testing is a basic search paradigm that occurs in a variety of situations such as quality control in product testing, searching in storage systems, multiple access communications, and software testing, among the others. Group testing procedures have been recently applied in Computational Molecular Biology, where they are used for screening library 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 \( \mathcal{P} \), and an optimal algorithm for the case in which the outcome of tests may be unreliable because of the presence of “inhibitory” items in \( \mathcal{O} \). Our results depend on a combinatorial structure introduced in this paper. We believe that it will prove useful in other contexts too.

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica ed Applicazioni, Università di Salerno, 84081, Baronissi (SA), Italy

    Annalisa De Bonis & Ugo Vaccaro

  2. Department of Computer Science, The University of Liverpool, Liverpool, L69 7ZF, UK

    Leszek Gąsieniec

Authors
  1. Annalisa De Bonis
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  2. Leszek Gąsieniec
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  3. Ugo Vaccaro
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Editor information

Editors and Affiliations

  1. Dept. of Mathematics and Computer Science, Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Jos C. M. Baeten

  2. School of Industrial and Systems Engineering, Georgia Institute of Technology, 765 Ferst Drive, Atlanta, GA, 30332-0205, USA

    Jan Karel Lenstra

  3. Department of Information Technology, Uppsala University, P.O. Box 337, 75105, Uppsala, Sweden

    Joachim Parrow

  4. Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    Gerhard J. Woeginger

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© 2003 Springer-Verlag Berlin Heidelberg

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De Bonis, A., Gąsieniec, L., Vaccaro, U. (2003). Generalized Framework for Selectors with Applications in Optimal Group Testing. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds) Automata, Languages and Programming. ICALP 2003. Lecture Notes in Computer Science, vol 2719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45061-0_8

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  • DOI: https://doi.org/10.1007/3-540-45061-0_8

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