Fast splitting algorithms for sparsity-constrained and noisy group testing

Author:

Price Eric1,Scarlett Jonathan2,Tan Nelvin3

Affiliation:

1. Department of Computer Science, University of Texas at Austin , Austin, TX 78712, USA

2. Department of Computer Science, National University of Singapore , 117417 Singapore; Department of Mathematics, National University of Singapore, 119076 Singapore; Institute of Data Science, National University of Singapore, 117602 Singapore

3. Department of Engineering, University of Cambridge , Cambridge CB2 1PZ, UK

Abstract

Abstract In group testing, the goal is to identify a subset of defective items within a larger set of items based on tests whose outcomes indicate whether at least one defective item is present. This problem is relevant in areas such as medical testing, DNA sequencing, communication protocols and many more. In this paper, we study (i) a sparsity-constrained version of the problem, in which the testing procedure is subjected to one of the following two constraints: items are finitely divisible and thus may participate in at most $\gamma $ tests; or tests are size-constrained to pool no more than $\rho $ items per test; and (ii) a noisy version of the problem, where each test outcome is independently flipped with some constant probability. Under each of these settings, considering the for-each recovery guarantee with asymptotically vanishing error probability, we introduce a fast splitting algorithm and establish its near-optimality not only in terms of the number of tests, but also in terms of the decoding time. While the most basic formulations of our algorithms require $\varOmega (n)$ storage for each algorithm, we also provide low-storage variants based on hashing, with similar recovery guarantees.

Funder

National Science Foundation

National University of Singapore

Publisher

Oxford University Press (OUP)

Subject

Applied Mathematics,Computational Theory and Mathematics,Numerical Analysis,Statistics and Probability,Analysis

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