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On the optimality of some group testing algorithms
Matthew Aldridge · 2017-05-08 · via math.PR updates on arXiv.org

We consider Bernoulli nonadaptive group testing with $k = Θ(n^θ)$ defectives, for $θ\in (0,1)$. The practical definite defectives (DD) detection algorithm is known to be optimal for $θ\geq 1/2$. 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 $θ\geq 1/2$.

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