Sparse Identification for Automatic Large-Scale Screening: A Constraint-Aware Framework with Ultra Fast Decoding Algorithm

In the early stages of a pandemic, identification of a small number of infected individuals through large-scale screening is critical for pandemic control, yet remains challenging under limited reagents and testing capacity. Existing group testing methods suffer from either high computational complexity or low identification accuracy. Even worse, no available methods provide theoretically rigorous analysis for sparse identification with hard constraints caused by the sample usage constraint and the dilution effect existing ubiquitously in practical applications. In this article, we propose the Logic Screening method (LoSc), an ultra fast, accurate, and theoretically grounded framework for large-scale screening. LoSc introduces a novel decoding algorithm with a very simple selection strategy, achieving identification of all positives with only O(klogn) pooled tests. The decoding relies only on logical operations, enabling direct hardware implementation and yielding ultra fast computational implementation. Moreover, LoSc explicitly incorporates dilution and sample usage constraints into pooling designs, and establishes theoretical guarantees to guide optimal pooling configurations. Extensive simulations confirm the superior effectiveness, efficiency, and scalability. We believe LoSc offers a fast and reliable solution for automatic large-scale screening.