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RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2020.13
A Fast Binary Splitting Approach to Non-Adaptive Group Testing

Authors: Eric Price and Jonathan Scarlett

Published in: LIPIcs, Volume 176, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)

Abstract
In this paper, we consider the problem of noiseless non-adaptive group testing under the for-each recovery guarantee, also known as probabilistic group testing. In the case of n items and k defectives, we provide an algorithm attaining high-probability recovery with O(k log n) scaling in both the number of tests and runtime, improving on the best known O(k² log k ⋅ log n) runtime previously available for any algorithm that only uses O(k log n) tests. Our algorithm bears resemblance to Hwang’s adaptive generalized binary splitting algorithm (Hwang, 1972); we recursively work with groups of items of geometrically vanishing sizes, while maintaining a list of "possibly defective" groups and circumventing the need for adaptivity. While the most basic form of our algorithm requires Ω(n) storage, we also provide a low-storage variant based on hashing, with similar recovery guarantees.
Cite as

Eric Price and Jonathan Scarlett. A Fast Binary Splitting Approach to Non-Adaptive Group Testing. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 176, pp. 13:1-13:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{price_et_al:LIPIcs.APPROX/RANDOM.2020.13,
  author =	{Price, Eric and Scarlett, Jonathan},
  title =	{{A Fast Binary Splitting Approach to Non-Adaptive Group Testing}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)},
  pages =	{13:1--13:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-164-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{176},
  editor =	{Byrka, Jaros{\l}aw and Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2020.13},
  URN =		{urn:nbn:de:0030-drops-126165},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2020.13},
  annote =	{Keywords: Group testing, sparsity, sublinear-time decoding, binary splitting}
}
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