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Bounds for the Number of Tests in Non-adaptive Randomized Algorithms for Group Testing

  • Nader H. Bshouty
  • George Haddad
  • Catherine A. Haddad-ZaknoonEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12011)

Abstract

We study the group testing problem with non-adaptive randomized algorithms. Several models have been discussed in the literature to determine how to randomly choose the tests. For a model \(\mathcal{M}\), let \(m_\mathcal{M}(n,d)\) be the minimum number of tests required to detect at most d defectives within n items, with success probability at least \(1-\delta \), for some constant \(\delta \). In this paper, we study the measures
$$c_\mathcal{M}(d)=\lim _{n\rightarrow \infty } \frac{m_\mathcal{M}(n,d)}{\ln n} \text{ and } \ c_\mathcal{M}=\lim _{d\rightarrow \infty } \frac{c_\mathcal{M}(d)}{d}.$$
In the literature, the analyses of such models only give upper bounds for \(c_\mathcal{M}(d)\) and \(c_\mathcal{M}\), and for some of them, the bounds are not tight. We give new analyses that yield tight bounds for \(c_\mathcal{M}(d)\) and \(c_\mathcal{M}\) for all the known models \(\mathcal{M}\).

Keywords

Group testing Randomized algorithms Non-adaptive algorithms 

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Nader H. Bshouty
    • 1
  • George Haddad
    • 2
  • Catherine A. Haddad-Zaknoon
    • 1
    Email author
  1. 1.TechnionHaifaIsrael
  2. 2.The Orthodox Arab College, Grade 11HaifaIsrael

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