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Information-Theoretic and Algorithmic Thresholds for Group Testing

Authors Amin Coja-Oghlan, Oliver Gebhard, Max Hahn-Klimroth, Philipp Loick

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ACM Subject Classification
  • Theory of computation → Theory and algorithms for application domains
  • Theory of computation → Bayesian analysis
  • Theory of computation → Machine learning theory
Keywords
  • Group testing problem
  • phase transitions
  • information theory
  • efficient algorithms
  • sharp threshold
  • Bayesian inference

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Abstract

In the group testing problem we aim to identify a small number of infected individuals within a large population. We avail ourselves to a procedure that can test a group of multiple individuals, with the test result coming out positive iff at least one individual in the group is infected. With all tests conducted in parallel, what is the least number of tests required to identify the status of all individuals? In a recent test design [Aldridge et al. 2016] the individuals are assigned to test groups randomly, with every individual joining an equal number of groups. We pinpoint the sharp threshold for the number of tests required in this randomised design so that it is information-theoretically possible to infer the infection status of every individual. Moreover, we analyse two efficient inference algorithms. These results settle conjectures from [Aldridge et al. 2014, Johnson et al. 2019].

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Amin Coja-Oghlan, Oliver Gebhard, Max Hahn-Klimroth, and Philipp Loick. Information-Theoretic and Algorithmic Thresholds for Group Testing. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 43:1-43:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.ICALP.2019.43

Author Details

Amin Coja-Oghlan
  • Goethe University, Frankfurt, Germany
Oliver Gebhard
  • Goethe University, Frankfurt, Germany
Max Hahn-Klimroth
  • Goethe University, Frankfurt, Germany
Philipp Loick
  • Goethe University, Frankfurt, Germany

Funding

  • Coja-Oghlan, Amin: Supported of DFG 646/3.
  • Hahn-Klimroth, Max: Supported by Stiftung Polytechnische Gesellschaft.
  • Loick, Philipp: Supported of DFG 646/3.

Acknowledgements

We thank Arya Mazumdar for bringing the group testing problem to our attention.

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