Paligadu, V., Johnson, O. and Aldridge, M. orcid.org/0000-0002-9347-1586 (2024) Small Error Algorithms for Tropical Group Testing. IEEE Transactions on Information Theory, 70 (10). pp. 7232-7250. ISSN 0018-9448
Abstract
We consider a version of the classical group testing problem motivated by PCR testing for COVID-19. In the so-called tropical group testing model, the outcome of a test is the lowest cycle threshold (Ct) level of the individuals pooled within it, rather than a simple binary indicator variable. We introduce the tropical counterparts of three classical non-adaptive algorithms (COMP, DD and SCOMP), and analyse their behaviour through both simulations and bounds on error probabilities. By comparing the results of the tropical and classical algorithms, we gain insight into the extra information provided by learning the outcomes (Ct levels) of the tests. We show that in a limiting regime the tropical COMP algorithm requires as many tests as its classical counterpart, but that for sufficiently dense problems tropical DD can recover more information with fewer tests, and can be viewed as essentially optimal in certain regimes.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2024 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. |
Keywords: | Group testing, polymerase chain reaction (PCR) testing, tropical arithmetic |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 17 Oct 2024 09:05 |
Last Modified: | 17 Oct 2024 09:05 |
Status: | Published |
Publisher: | Institute of Electrical and Electronics Engineers (IEEE) |
Identification Number: | 10.1109/tit.2024.3445271 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:218504 |