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Title: Optimal Nested Test Plan for Combinatorial Quantitative Group Testing

Abstract

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.

Authors:
ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [2]
  1. Cornell Univ., Ithaca, NY (United States)
  2. Univ. of California, Davis, CA (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1526506
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
IEEE Transactions on Signal Processing
Additional Journal Information:
Journal Volume: 66; Journal Issue: 4; Journal ID: ISSN 1053-587X
Publisher:
IEEE
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; group testing; adaptive test plan; heavy hitter detection; anomaly detection; traffic measurements; spectrum sensing

Citation Formats

Wang, Chao, Zhao, Qing, and Chuah, Chen -Nee. Optimal Nested Test Plan for Combinatorial Quantitative Group Testing. United States: N. p., 2017. Web. doi:10.1109/TSP.2017.2780053.
Wang, Chao, Zhao, Qing, & Chuah, Chen -Nee. Optimal Nested Test Plan for Combinatorial Quantitative Group Testing. United States. doi:10.1109/TSP.2017.2780053.
Wang, Chao, Zhao, Qing, and Chuah, Chen -Nee. Mon . "Optimal Nested Test Plan for Combinatorial Quantitative Group Testing". United States. doi:10.1109/TSP.2017.2780053. https://www.osti.gov/servlets/purl/1526506.
@article{osti_1526506,
title = {Optimal Nested Test Plan for Combinatorial Quantitative Group Testing},
author = {Wang, Chao and Zhao, Qing and Chuah, Chen -Nee},
abstractNote = {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.},
doi = {10.1109/TSP.2017.2780053},
journal = {IEEE Transactions on Signal Processing},
number = 4,
volume = 66,
place = {United States},
year = {2017},
month = {12}
}

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