Group Testing on General Set-Systems
Mira Gonen, Michael Langberg, Alex Sprintson

TL;DR
This paper extends group testing to a generalized set-system framework modeled by hypergraphs, aiming to reduce tests needed by leveraging additional structure, with complexity results and near-optimal solutions for adaptive and non-adaptive scenarios.
Contribution
It introduces a generalized group testing model based on arbitrary set-systems, analyzes its computational complexity, and provides near-optimal testing strategies.
Findings
Finding NP-hardness for optimal solutions in the non-adaptive case.
Proposing a testing scheme with $O(d\, ext{log}|E|)$ tests.
Achieving order-optimal tests for hypergraphs with large symmetric differences.
Abstract
Group testing is one of the fundamental problems in coding theory and combinatorics in which one is to identify a subset of contaminated items from a given ground set. There has been renewed interest in group testing recently due to its applications in diagnostic virology, including pool testing for the novel coronavirus. The majority of existing works on group testing focus on the \emph{uniform} setting in which any subset of size from a ground set of size is potentially contaminated. In this work, we consider a {\em generalized} version of group testing with an arbitrary set-system of potentially contaminated sets. The generalized problem is characterized by a hypergraph , where represents the ground set and edges represent potentially contaminated sets. The problem of generalized group testing is motivated by practical settings in which not all…
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Taxonomy
TopicsSARS-CoV-2 detection and testing · Immunodeficiency and Autoimmune Disorders · HIV Research and Treatment
