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An efficient FPRAS type group testing procedure to approximate the number of defectives

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Abstract

In many fault detection problems, we want to detect or identify defective items in a sample set by 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. Another practically important problem is to estimate the number of defective items in a sample set. In this paper, we present an efficient FPRAS (fully polynomial-time randomized approximation scheme) type group testing procedure to approximate the number of defective items in a sample set.

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Acknowledgements

The authors would like to thank the anonymous reviewers for their helpful comments and suggestions.

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Authors and Affiliations

  1. School of Management, Xi’an Jiaotong University, Xi’an, 710049, China

    Yongxi Cheng & Yinfeng Xu

  2. State Key Lab for Manufacturing Systems Engineering, Xi’an, 710049, China

    Yinfeng Xu

  3. Ministry of Education Key Lab for Process Control & Efficiency Engineering, Xi’an, 710049, China

    Yinfeng Xu

Authors
  1. Yongxi Cheng
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  2. Yinfeng Xu
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Corresponding author

Correspondence to Yongxi Cheng.

Additional information

This work was partially supported by the National Natural Science Foundation of China under Grant Nos. 11101326, 71071123, 60921003, and the Program for Changjiang Scholars and Innovative Research Team in University (IRT1173).

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Cheng, Y., Xu, Y. An efficient FPRAS type group testing procedure to approximate the number of defectives. J Comb Optim 27, 302–314 (2014). https://doi.org/10.1007/s10878-012-9516-5

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  • DOI: https://doi.org/10.1007/s10878-012-9516-5

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