Concomitant Group Testing

• URL: http://arxiv.org/abs/2309.04221v1
• Date: Fri, 8 Sep 2023 09:11:12 GMT
• Title: Concomitant Group Testing
• Authors: Thach V. Bui, Jonathan Scarlett
• Abstract summary: We introduce a variation of the group testing problem capturing the idea that a positive test requires a combination of multiple types'' of item. The goal is to reliably identify all of the semi-defective sets using as few tests as possible. Our algorithms are distinguished by (i) whether they are deterministic (zero-error) or randomized (small-error), and (ii) whether they are non-adaptive, fully adaptive, or have limited adaptivity.
• Score: 49.50984893039441
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we introduce a variation of the group testing problem capturing the idea that a positive test requires a combination of multiple ``types'' of item. Specifically, we assume that there are multiple disjoint \emph{semi-defective sets}, and a test is positive if and only if it contains at least one item from each of these sets. The goal is to reliably identify all of the semi-defective sets using as few tests as possible, and we refer to this problem as \textit{Concomitant Group Testing} (ConcGT). We derive a variety of algorithms for this task, focusing primarily on the case that there are two semi-defective sets. Our algorithms are distinguished by (i) whether they are deterministic (zero-error) or randomized (small-error), and (ii) whether they are non-adaptive, fully adaptive, or have limited adaptivity (e.g., 2 or 3 stages). Both our deterministic adaptive algorithm and our randomized algorithms (non-adaptive or limited adaptivity) are order-optimal in broad scaling regimes of interest, and improve significantly over baseline results that are based on solving a more general problem as an intermediate step (e.g., hypergraph learning).

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