Improved group testing rates with constant column weight designs

TL;DR

This paper demonstrates that using constant column weight designs in nonadaptive group testing improves detection rates over Bernoulli designs, achieving significant performance gains with practical algorithms across various sparsity regimes.

Contribution

It introduces constant column weight testing matrices for nonadaptive group testing, showing improved rates and performance over traditional Bernoulli designs, including algorithm-independent bounds.

Findings

COMP detection rate increased by 31% with constant column weight designs

Outperforms Bernoulli designs in dense and sparse regimes

Provides an algorithm-independent upper bound showing similar improvements

Abstract

We consider nonadaptive group testing where each item is placed in a constant number of tests. The tests are chosen uniformly at random with replacement, so the testing matrix has (almost) constant column weights. We show that performance is improved compared to Bernoulli designs, where each item is placed in each test independently with a fixed probability. In particular, we show that the rate of the practical COMP detection algorithm is increased by 31% in all sparsity regimes. In dense cases, this beats the best possible algorithm with Bernoulli tests, and in sparse cases is the best proven performance of any practical algorithm. We also give an algorithm-independent upper bound for the constant column weight case; for dense cases this is again a 31% increase over the analogous Bernoulli result.