Application-oriented mathematical algorithms for group testing

Group testing is a widely used protocol which aims to test a small group of people to identify whether at least one of them is infected. It is particularly efficient if the infection rate is low, because it only requires a single test if everybody in the group is negative. The most efficient use of group testing is a complex mathematical question. However, the answer highly depends on practical parameters and restrictions, which are partially ignored by the mathematical literature. This paper aims to offer practically efficient group testing algorithms, focusing on the current COVID-19 epidemic.

Optimal Pool Size for COVID-19 Group Testing

This paper presents an analytical formulation for determining optimal pool size in the initial pooling stage and the subsequent retests for COVID-19. A generalized constant compaction approach confirms the efficiency of “halving” targeted population between retest stages. An analytical gain formula is derived to aid future test designs. It is observed that optimal gain relies on the proper choice of the initial pool size. This optimal compaction scheme outperforms the conventional algorithms in most cases and may provide a mathematically-native road map for us to operate beyond the standard super-even-number-based (64, 32, 16, 8…, 1) group testing algorithms.

Cutting testing costs by the pooling design

Introduction/purpose: The purpose of group testing algorithms is to provide a more rational resource usage. Therefore, it is expected to improve the efficiency of large-scale COVID-19 screening as well. Methods: Two variants of non-adaptive group testing approaches are presented: Hwang's generalized binary-splitting algorithm and the matrix strategy. Results: The positive and negative sides of both approaches are discussed. Also, the estimations of the maximum number of tests are given. The matrix strategy is presented with a particular modification which reduces the corresponding estimation of the maximum number of tests and which does not affect the complexity of the procedure. This modification can be interesting from the applicability viewpoint. Conclusion: Taking into account the current situation, it makes sense to consider these methods in order to achieve some resource cuts in testing, thus making the epidemiological measures more efficient than they are now.