Lower Bound for Non-Adaptive Estimation of the Number of Defective Items

Author Nader H. Bshouty

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Nader H. Bshouty
  • Department of Computer Science, Technion, Haifa, Israel

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Nader H. Bshouty. Lower Bound for Non-Adaptive Estimation of the Number of Defective Items. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 2:1-2:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


We prove that to estimate within a constant factor the number of defective items in a non-adaptive randomized group testing algorithm we need at least Omega~(log n) tests. This solves the open problem posed by Damaschke and Sheikh Muhammad in [Peter Damaschke and Azam Sheikh Muhammad, 2010; Peter Damaschke and Azam Sheikh Muhammad, 2010].

Subject Classification

ACM Subject Classification
  • Mathematics of computing
  • Mathematics of computing → Discrete mathematics
  • Mathematics of computing → Probabilistic algorithms
  • Theory of computation → Probabilistic computation
  • Group Testing
  • Estimation
  • Defective Items


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