Generalized Group Testing
Xiwei Cheng, Sidharth Jaggi, Qiaoqiao Zhou

TL;DR
This paper introduces a generalized group testing framework that models various noisy and noiseless scenarios using a stochastic test function, providing new bounds and schemes for efficient identification of defectives.
Contribution
It develops a non-adaptive testing scheme applicable to a broad class of models with theoretical bounds on the number of tests needed.
Findings
The proposed scheme identifies defectives with high probability using ${ m O}(H(f) d \log(n/\varepsilon))$ tests.
Any non-adaptive scheme requires at least ${\Omega}((1-\varepsilon) h(f) d \log(n/d))$ tests.
The sensitivity and concentration parameters relate as $H(f)/h(f) \in \Theta(1)$ for many models.
Abstract
In the problem of classical group testing one aims to identify a small subset (of size ) diseased individuals/defective items in a large population (of size ). This process is based on a minimal number of suitably-designed group tests on subsets of items, where the test outcome is positive iff the given test contains at least one defective item. Motivated by physical considerations, we consider a generalized setting that includes as special cases multiple other group-testing-like models in the literature. In our setting, which subsumes as special cases a variety of noiseless and noisy group-testing models in the literature, the test outcome is positive with probability , where is the number of defectives tested in a pool, and is an arbitrary monotonically increasing (stochastic) test function. Our main contributions are as follows. 1. We present a…
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Taxonomy
TopicsSARS-CoV-2 detection and testing · Advanced biosensing and bioanalysis techniques · Biosensors and Analytical Detection
