Efficient and Accurate Group Testing via Belief Propagation: An Empirical Study

Authors Amin Coja-Oghlan, Max Hahn-Klimroth, Philipp Loick, Manuel Penschuck

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Amin Coja-Oghlan
  • Faculty of Computer Science, TU Dortmund, Germany
Max Hahn-Klimroth
  • Faculty of Computer Science, TU Dortmund, Germany
Philipp Loick
  • Institute for Mathematics, Goethe Universität, Frankfurt am Main, Germany
Manuel Penschuck
  • Faculty of Computer Science, Goethe Universität, Frankfurt am Main, Germany

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Amin Coja-Oghlan, Max Hahn-Klimroth, Philipp Loick, and Manuel Penschuck. Efficient and Accurate Group Testing via Belief Propagation: An Empirical Study. In 20th International Symposium on Experimental Algorithms (SEA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 233, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


The group testing problem asks for efficient pooling schemes and inference algorithms that allow to screen moderately large numbers of samples for rare infections. The goal is to accurately identify the infected individuals while minimizing the number of tests. We propose the novel adaptive pooling scheme adaptive Belief Propagation (ABP) that acknowledges practical limitations such as limited pooling sizes and noisy tests that may give imperfect answers. We demonstrate that the accuracy of ABP surpasses that of individual testing despite using few overall tests. The new design comes with Belief Propagation as an efficient inference algorithm. While the development of ABP is guided by mathematical analyses and asymptotic insights, we conduct an experimental study to obtain results on practical population sizes.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Probabilistic inference problems
  • Mathematics of computing → Random graphs
  • Mathematics of computing → Coding theory
  • Group testing
  • Probabilistic Construction
  • Belief Propagation
  • Simulation


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