A new randomized algorithm for group testing with unknown number of defective items

Yongxi Cheng (), Jue Guo () and Feifeng Zheng ()
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Yongxi Cheng: School of Management, Xi’an Jiaotong University
Jue Guo: School of Management, Xi’an Jiaotong University
Feifeng Zheng: Glorious Sun School of Business and Management, Donghua University

Journal of Combinatorial Optimization, 2015, vol. 30, issue 1, No 12, 150-159

Abstract: Abstract In many fault detection problems, we want to identify defective items from a set of $$n$$ n items using the minimum number of tests. Group testing is for the scenario where each test is on a subset of items, and tells whether the subset contains at least one defective item or not. In practice, the number $$d$$ d of defective items is often unknown in advance. In this paper, we propose a new randomized group testing algorithm RPT (Randomized Parallel Testing) for the case where the number $$d$$ d of defective items is unknown in advance, such that with high probability $$1-\frac{1}{(2d)^{\Omega (1)}}$$ 1 - 1 ( 2 d ) Ω ( 1 ) , the total number of tests performed by RPT is bounded from the above by $$d\log \frac{n}{d}+2d+O(d^{\frac{2}{3}}\log d)$$ d log n d + 2 d + O ( d 2 3 log d ) . If $$0

Keywords: Fault detection; Group testing; Randomized algorithms; Approximation (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10878-013-9640-x

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