On the optimality of some group testing algorithms

Matthew Aldridge

doi:10.1109/isit.2017.8007097

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arXiv · 1705.02708

On the optimality of some group testing algorithms

Matthew Aldridge

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Abstract

We consider Bernoulli nonadaptive group testing with $k = \Theta(n^\theta)$ defectives, for $\theta \in (0,1)$. The practical definite defectives (DD) detection algorithm is known to be optimal for $\theta \geq 1/2$. We give a new upper bound on the rate of DD, showing that DD is strictly suboptimal for $\theta < 0.41$. 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 $\theta \geq 1/2$.

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Matthew Aldridge. 2017-05-07. On the optimality of some group testing algorithms. https://doi.org/10.1109/isit.2017.8007097

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