Optimal Pooling Matrix Design for Group Testing with Dilution (Row Degree) Constraints

Jirong Yi; Myung Cho; Xiaodong Wu; Raghu Mudumbai; Weiyu Xu

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Optimal Pooling Matrix Design for Group Testing with Dilution (Row Degree) Constraints

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Optimal Pooling Matrix Design for Group Testing with Dilution (Row Degree) Constraints

Jirong Yi, Myung Cho, Xiaodong Wu, Raghu Mudumbai and Weiyu Xu

ArXiv.org

08/05/2020

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https://arxiv.org/abs/2008.01944View

Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

In this paper, we consider the problem of designing optimal pooling matrix for group testing (for example, for COVID-19 virus testing) with the constraint that no more than r>0 samples can be pooled together, which we call "dilution constraint". This problem translates to designing a matrix with elements being either 0 or 1 that has no more than r '1's in each row and has a certain performance guarantee of identifying anomalous elements. We explicitly give pooling matrix designs that satisfy the dilution constraint and have performance guarantees of identifying anomalous elements, and prove their optimality in saving the largest number of tests, namely showing that the designed matrices have the largest width-to-height ratio among all constraint-satisfying 0-1 matrices.

Details

Title: Subtitle: Optimal Pooling Matrix Design for Group Testing with Dilution (Row Degree) Constraints
Creators: Jirong Yi
Myung Cho
Xiaodong Wu
Raghu Mudumbai
Weiyu Xu
Resource Type: Preprint
Publication Details: ArXiv.org
ISSN: 2331-8422
Language: English
Date posted: 08/05/2020
Academic Unit: Electrical and Computer Engineering; Radiation Oncology; The Iowa Institute for Biomedical Imaging
Record Identifier: 9984198014002771

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