Small error algorithms for tropical group testing

TL;DR

This paper explores tropical group testing, a variant of classical group testing using Ct levels from PCR tests, introducing new algorithms and analyzing their efficiency and information gain.

Contribution

It introduces tropical versions of classical algorithms and analyzes their performance, revealing advantages in dense problem regimes and insights into information content.

Findings

Tropical COMP requires similar tests as classical in the limit.

Tropical DD can outperform classical in dense regimes.

Tropical DD is nearly optimal under certain conditions.

Abstract

We consider a version of the classical group testing problem motivated by PCR testing for COVID-19. In the so-called tropical group testing model, the outcome of a test is the lowest cycle threshold (Ct) level of the individuals pooled within it, rather than a simple binary indicator variable. We introduce the tropical counterparts of three classical non-adaptive algorithms (COMP, DD and SCOMP), and analyse their behaviour through both simulations and bounds on error probabilities. By comparing the results of the tropical and classical algorithms, we gain insight into the extra information provided by learning the outcomes (Ct levels) of the tests. We show that in a limiting regime the tropical COMP algorithm requires as many tests as its classical counterpart, but that for sufficiently dense problems tropical DD can recover more information with fewer tests, and can be viewed as essentially optimal in certain regimes.