Johnson, O, Aldridge, M orcid.org/0000-0002-9347-1586 and Scarlett, J (2019) Performance of Group Testing Algorithms With Near-Constant Tests-per-Item. IEEE Transactions on Information Theory, 65 (2). pp. 707-723. ISSN 0018-9448
Abstract
We consider the nonadaptive group testing with N items, of which K = Θ(Nθ) are defective. We study a test design in which each item appears in nearly the same number of tests. For each item, we independently pick L tests uniformly at random with replacement, and place the item in those tests. We analyse the performance of these designs with simple and practical decoding algorithms in a range of sparsity regimes, and show that the performance is consistently improved in comparison with standard Bernoulli designs.We show that our new design requires roughly 23% fewer tests than a Bernoulli design when paired with the simple decoding algorithms known as COMP and DD. This gives the best known nonadaptive group testing performance for θ > 0:43, and the best proven performance with a practical decoding algorithm for all θ ∈ (0, 1). We also give a converse result showing that the DD algorithm is optimal with respect to our randomised design when θ > 1/2. We complement our theoretical results with simulations that show a notable improvement over Bernoulli designs in both sparse and dense regimes.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 IEEE. This is an author produced version of a paper published in IEEE Transactions on Information Theory. 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. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Algorithm design and analysis; group testing; measurement design; performance bounds; sparse models |
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: | 02 Nov 2018 15:57 |
Last Modified: | 31 Jan 2020 14:52 |
Status: | Published |
Publisher: | IEEE |
Identification Number: | 10.1109/TIT.2018.2861772 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:137695 |