Non-Adaptive Group Testing with Inhibitors

TL;DR

This paper introduces a probabilistic non-adaptive pooling design for group testing with inhibitors, achieving near-optimal test complexity in certain regimes and providing efficient decoding algorithms.

Contribution

It proposes a novel non-adaptive pooling scheme with low complexity decoding for GTI, matching lower bounds in some regimes and extending to cases with only bounds on defectives and inhibitors.

Findings

Sample complexity scales as O(d log n) and O(r^2 / d log n) in different regimes.

Number of tests meets lower bounds in some regimes, exceeding them by a logarithmic factor in others.

Decoding algorithms have a time complexity of O(nT).

Abstract

Group testing with inhibitors (GTI) introduced by Farach at al. is studied in this paper. There are three types of items, $d$ defectives, $r$ inhibitors and $n-d-r$ normal items in a population of $n$ items. The presence of any inhibitor in a test can prevent the expression of a defective. For this model, we propose a probabilistic non-adaptive pooling design with a low complexity decoding algorithm. We show that the sample complexity of the number of tests required for guaranteed recovery with vanishing error probability using the proposed algorithm scales as $T=O(d \log n)$ and $T=O(\frac{r^2}{d}\log n)$ in the regimes $r=O(d)$ and $d=o(r)$ respectively. In the former regime, the number of tests meets the lower bound order while in the latter regime, the number of tests is shown to exceed the lower bound order by a $\log \frac{r}{d}$ multiplicative factor. When only upper bounds on the number of defectives $D$ and the number of inhibitors $R$ are given instead of their exact values, the sample complexity of the number of tests using the proposed algorithm scales as $T=O(D \log n)$ and $T=O(R^2 \log n)$ in the regimes $R^2=O(D)$ and $D=o(R^2)$ respectively. In the former regime, the number of tests meets the lower bound order while in the latter regime, the number of tests exceeds the lower bound order by a $\log R$ multiplicative factor. The time complexity of the proposed decoding algorithms scale as $O(nT)$.