Optimal Nested Test Plan for Combinatorial Quantitative Group Testing

Journal Article · 04 December 2017 · IEEE Transactions on Signal Processing

DOI: https://doi.org/10.1109/TSP.2017.2780053 · OSTI ID:1526506

Wang, Chao  ^[1]; Zhao, Qing  ^[1]; Chuah, Chen -Nee  ^[2]

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1. Cornell Univ., Ithaca, NY (United States)
2. Univ. of California, Davis, CA (United States)

We consider the quantitative group testing problem where the objective is to identify defective items in a given population based on results of tests performed on subsets of the population. Under the quantitative group testing model, the result of each test reveals the number of defective items in the tested group. The minimum number of tests achievable by nested test plans was established by Aigner and Schughart in 1985 within a minimax framework. Furthermore, the optimal nested test plan offering this performance, however, was not obtained. In this paper, we establish the optimal nested test plan in a closed form. This optimal nested test plan is also order optimal among all test plans as the population size approaches infinity. Using heavy-hitter detection as a case study, we show via simulation examples orders of magnitude improvement of the group testing approach over two prevailing sampling-based approaches in detection accuracy and counter consumption. Other applications include anomaly detection and wideband spectrum sensing in cognitive radio systems.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• Grant/Contract Number: AC02-05CH11231
• OSTI ID: 1526506
• Journal Information: IEEE Transactions on Signal Processing, Journal Name: IEEE Transactions on Signal Processing Journal Issue: 4 Vol. 66; ISSN 1053-587X
• Publisher: IEEECopyright Statement
• Country of Publication: United States
• Language: English