Group testing algorithms: bounds and simulations

TL;DR

This paper analyzes non-adaptive noiseless group testing algorithms, introducing new methods and comparing their theoretical limits and simulation performance, highlighting the advantages of DD and SCOMP over COMP.

Contribution

The paper introduces two new algorithms, DD and SCOMP, and provides bounds and simulations showing their effectiveness compared to existing methods.

Findings

DD outperforms COMP in asymptotic rate

DD is nearly optimal when K ≥ √N

SCOMP closely approaches the optimal SSS in simulations

Abstract

We consider the problem of non-adaptive noiseless group testing of $N$ items of which $K$ are defective. We describe four detection algorithms: the COMP algorithm of Chan et al.; two new algorithms, DD and SCOMP, which require stronger evidence to declare an item defective; and an essentially optimal but computationally difficult algorithm called SSS. By considering the asymptotic rate of these algorithms with Bernoulli designs we see that DD outperforms COMP, that DD is essentially optimal in regimes where $K \geq \sqrt N$, and that no algorithm with a nonadaptive Bernoulli design can perform as well as the best non-random adaptive designs when $K > N^{0.35}$. In simulations, we see that DD and SCOMP far outperform COMP, with SCOMP very close to the optimal SSS, especially in cases with larger $K$.