IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i4p637-d348606.html
   My bibliography  Save this article

Theoretical Bounds on Performance in Threshold Group Testing Schemes

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/4/637/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/4/637/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jing Gai & Mohan Chaudhry, 2024. "Relations among the Queue-Length Probabilities in the Pre-Arrival, Random, and Post-Departure Epochs in the GI/M a , b /c Queue," Mathematics, MDPI, vol. 12(17), pages 1-8, August.
    2. Shaul K. Bar-Lev & Wolfgang Stadje & Frank A. van der Duyn Schouten, 2004. "Optimal Group Testing with Processing Times and Incomplete Identification," Methodology and Computing in Applied Probability, Springer, vol. 6(1), pages 55-72, March.
    3. Shaul K. Bar‐Lev & Onno Boxma & Andreas Löpker & Wolfgang Stadje & Frank A. Van der Duyn Schouten, 2012. "Group testing procedures with quantitative features and incomplete identification," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(1), pages 39-51, February.
    4. Shaul K. Bar-Lev & Hans Blanc & Onno Boxma & Guido Janssen & David Perry, 2013. "Tandem Queues with Impatient Customers for Blood Screening Procedures," Methodology and Computing in Applied Probability, Springer, vol. 15(2), pages 423-451, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:637-:d:348606. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.