On the optimality of some group testing algorithms

Abstract

We consider Bernoulli nonadaptive group testing with k = Θ(ηθ) defectives, for θ (0,1). The practical definite defectives (DD) detection algorithm is known to be optimal for θ > 1/2. We give a new upper bound on the rate of DD, showing that DD is strictly suboptimal for θ < 0.41. We also show that the SCOMP algorithm and algorithms based on linear programming achieve a rate at least as high as DD, so in particular are also optimal for θ ≥ 1/2.

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Authors/Creators:	Aldridge, M https://orcid.org/0000-0002-9347-1586
Copyright, Publisher and Additional Information:	© 2017 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.
Dates:	Accepted: 1 April 2017 Published: 9 August 2017
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:	22 Nov 2018 13:55
Last Modified:	22 Nov 2018 13:55
Status:	Published
Publisher:	IEEE
Identification Number:	https://doi.org/10.1109/ISIT.2017.8007097

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On the optimality of some group testing algorithms

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