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Theoretical Bounds on Performance in Threshold Group Testing Schemes

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  • Jin-Taek Seong

    (Department of Convergence Software, Mokpo National University, Muan 58554, Korea)

Abstract

A threshold group testing (TGT) scheme with lower and upper thresholds is a general model of group testing (GT) which identifies a small set of defective samples. In this paper, we consider the TGT scheme that require the minimum number of tests. We aim to find lower and upper bounds for finding a set of defective samples in a large population. The decoding for the TGT scheme is exploited by minimization of the Hamming weight in channel coding theory and the probability of error is also defined. Then, we derive a new upper bound on the probability of error and extend a lower bound from conventional one to the TGT scheme. We show that the upper and lower bounds well match with each other at the optimal density ratio of the group matrix. In addition, we conclude that when the gaps between the two thresholds in the TGT framework increase, the group matrix with a high density should be used to achieve optimal performance.

Suggested Citation

  • Jin-Taek Seong, 2020. "Theoretical Bounds on Performance in Threshold Group Testing Schemes," Mathematics, MDPI, vol. 8(4), pages 1-13, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:637-:d:348606
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    References listed on IDEAS

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    1. Bar-Lev, Shaul K. & Boxma, Onno & Kleiner, Igor & Perry, David & Stadje, Wolfgang, 2017. "Recycled incomplete identification procedures for blood screening," European Journal of Operational Research, Elsevier, vol. 259(1), pages 330-343.
    2. Shaul K. Bar‐Lev & Arnon Boneh & David Perry, 1990. "Incomplete identification models for group‐testable items," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(5), pages 647-659, October.
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    Cited by:

    1. Jin-Taek Seong, 2022. "Theoretical Bounds on the Number of Tests in Noisy Threshold Group Testing Frameworks," Mathematics, MDPI, vol. 10(14), pages 1-14, July.
    2. Jin-Taek Seong, 2023. "Bounds on Performance for Recovery of Corrupted Labels in Supervised Learning: A Finite Query-Testing Approach," Mathematics, MDPI, vol. 11(17), pages 1-16, August.

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