Issue |
ESAIM: PS
Volume 26, 2022
|
|
---|---|---|
Page(s) | 283 - 303 | |
DOI | https://doi.org/10.1051/ps/2022007 | |
Published online | 16 June 2022 |
A tractable non-adaptative group testing method for non-binary measurements*
1
CIMAT, Guanajuato, Mexico
2
Université Sorbonne Paris Nord, LAGA, UMR 7539, 93430 Villetaneuse, France
3
DMA, École normale supérieure, Université PSL, 75005 Paris, France
** Corresponding author: mallein@math.univ-paris13.fr
Received:
9
June
2021
Accepted:
28
May
2022
The original problem of group testing consists in the identification of defective items in a collection, by applying tests on groups of items that detect the presence of at least one defective element in the group. The aim is then to identify all defective items of the collection with as few tests as possible. This problem is relevant in several fields, among which biology and computer sciences. In the present article we consider that the tests applied to groups of items returns a load, measuring how defective the most defective item of the group is. In this setting, we propose a simple non-adaptative algorithm allowing the detection of all defective items of the collection. Items are put on an n × n grid and pools are organised as lines, columns and diagonals of this grid. This method improves on classical group testing algorithms using only the binary response of the test. Group testing recently gained attraction as a potential tool to solve a shortage of COVID-19 test kits, in particular for RT-qPCR. These tests return the viral load of the sample and the viral load varies greatly among individuals. Therefore our model presents some of the key features of this problem. We aim at using the extra piece of information that represents the viral load to construct a one-stage pool testing algorithm on this idealized version. We show that under the right conditions, the total number of tests needed to detect contaminated samples can be drastically diminished.
Mathematics Subject Classification: 62B10 / 94C12
Key words: Group testing / one-stage algorithm / non-adaptative group testing / algorithm design and analysis / non binary test
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.