Tropical Group Testing

TL;DR

This paper introduces tropical group testing, a novel framework leveraging tropical arithmetic to improve COVID-19 testing efficiency and accuracy, especially with imprecise PCR measurements, outperforming traditional methods.

Contribution

The paper proposes tropical group testing, a new model that handles imprecise PCR data and reduces the number of tests needed compared to classical approaches.

Findings

Tropical group testing is more powerful than binary group testing.

It requires fewer tests than classical methods.

It can identify individual viral loads.

Abstract

Polymerase chain reaction (PCR) testing is the gold standard for diagnosing COVID-19. PCR amplifies the virus DNA 40 times to produce measurements of viral loads that span seven orders of magnitude. Unfortunately, the outputs of these tests are imprecise and therefore quantitative group testing methods, which rely on precise measurements, are not applicable. Motivated by the ever-increasing demand to identify individuals infected with SARS-CoV-19, we propose a new model that leverages tropical arithmetic to characterize the PCR testing process. Our proposed framework, termed tropical group testing, overcomes existing limitations of quantitative group testing by allowing for imprecise test measurements. In many cases, some of which are highlighted in this work, tropical group testing is provably more powerful than traditional binary group testing in that it require fewer tests than classical approaches, while additionally providing a mechanism to identify the viral load of each infected individual. It is also empirically stronger than related works that have attempted to combine PCR, quantitative group testing, and compressed sensing.