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A new strongly competitive group testing algorithm with small sequentiality

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  • Yongxi Cheng
  • Ding-Zhu Du
  • Feifeng Zheng

Abstract

In many fault detection problems, we want to identify all defective items from a sample set of items using the minimum number of tests. Group testing is for the scenario where each test is performed on a subset of items, and tells whether the subset contains at least one defective item or not. In practice, the number of defective items in the sample set is usually unknown. In this paper, we investigate new algorithms for the group testing problem with unknown number of defective items. We consider the scenario where the performance of a group testing algorithm is measured by two criteria: the primary criterion is the number of tests performed, which measures the total cost spent; and the secondary criterion is the number of stages the algorithm works in, which is referred to as the sequentiality of the algorithm in this paper and measures the minimum amount of time required by using the algorithm to identify all the defective items. We present a new algorithm Recursive Binary Splitting (RBS) for the above group testing problem with unknown number of defective items, and prove an upper bound on the number of tests required by RBS. The computational results show that RBS exhibits very good practical performance, measured in terms of both the above two criteria. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Yongxi Cheng & Ding-Zhu Du & Feifeng Zheng, 2015. "A new strongly competitive group testing algorithm with small sequentiality," Annals of Operations Research, Springer, vol. 229(1), pages 265-286, June.
    • Handle: RePEc:spr:annopr:v:229:y:2015:i:1:p:265-286:10.1007/s10479-014-1766-4
    DOI: 10.1007/s10479-014-1766-4
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    References listed on IDEAS

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    1. Yongxi Cheng & Ding-Zhu Du & Yinfeng Xu, 2014. "A Zig-Zag Approach for Competitive Group Testing," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 677-689, November.
    2. Lawrence M. Wein & Stefanos A. Zenios, 1996. "Pooled Testing for HIV Screening: Capturing the Dilution Effect," Operations Research, INFORMS, vol. 44(4), pages 543-569, August.
    3. Bar-Lev, Shaul K. & Parlar, Mahmut & Perry, David & Stadje, Wolfgang & Van der Duyn Schouten, Frank A., 2007. "Applications of bulk queues to group testing models with incomplete identification," European Journal of Operational Research, Elsevier, vol. 183(1), pages 226-237, November.
    4. Stuart Weele & Jose Ramirez-Marquez, 2011. "Optimization of container inspection strategy via a genetic algorithm," Annals of Operations Research, Springer, vol. 187(1), pages 229-247, July.
    5. Claeys, Dieter & Walraevens, Joris & Laevens, Koenraad & Bruneel, Herwig, 2010. "A queueing model for general group screening policies and dynamic item arrivals," European Journal of Operational Research, Elsevier, vol. 207(2), pages 827-835, December.
    6. Ana Concho & José Ramirez-Marquez, 2012. "Optimal design of container inspection strategies considering multiple objectives via an evolutionary approach," Annals of Operations Research, Springer, vol. 196(1), pages 167-187, July.
    7. Michael T. Goodrich & Daniel S. Hirschberg, 2008. "Improved adaptive group testing algorithms with applications to multiple access channels and dead sensor diagnosis," Journal of Combinatorial Optimization, Springer, vol. 15(1), pages 95-121, January.
    8. Lev Abolnikov & Alexander Dukhovny, 2003. "Optimization in HIV screening problems," International Journal of Stochastic Analysis, Hindawi, vol. 16, pages 1-14, January.
    9. Bar-Lev, S.K. & Parlar, M. & Perry, D. & Stadje, W. & van der Duyn Schouten, F.A., 2007. "Applications of bulk queues to group testing models with incomplete identification," Other publications TiSEM 0b1bfa5e-c1e6-43ec-9684-1, Tilburg University, School of Economics and Management.
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