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A Fast Binary Splitting Approach to Non-Adaptive Group Testing

Authors Eric Price, Jonathan Scarlett



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Author Details

Eric Price
  • Department of Computer Science, University of Texas at Austin, TX, USA
Jonathan Scarlett
  • Department of Computer Science & Department of Mathematics, National University of Singapore, Singapore

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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)
https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2020.13

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Group testing
  • sparsity
  • sublinear-time decoding
  • binary splitting

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