Semiquantitative Group Testing in at Most Two Rounds

TL;DR

This paper introduces new adaptive and nonadaptive semiquantitative group testing methods that efficiently identify defectives in two rounds, leveraging expander graphs and list-disjunct matrices for improved performance.

Contribution

It presents simple, effective 2-round and nonadaptive SQGT schemes using novel measurement matrix designs, addressing practical adaptive testing needs.

Findings

Significant improvement over existing SQGT schemes.

Efficient 2-round testing with practical applicability.

Use of expander graphs and list-disjunct matrices enhances performance.

Abstract

Semiquantitative group testing (SQGT) is a pooling method in which the test outcomes represent bounded intervals for the number of defectives. Alternatively, it may be viewed as an adder channel with quantized outputs. SQGT represents a natural choice for Covid-19 group testing as it allows for a straightforward interpretation of the cycle threshold values produced by polymerase chain reactions (PCR). Prior work on SQGT did not address the need for adaptive testing with a small number of rounds as required in practice. We propose conceptually simple methods for 2-round and nonadaptive SQGT that significantly improve upon existing schemes by using ideas on nonbinary measurement matrices based on expander graphs and list-disjunct matrices.