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Improved adaptive group testing algorithms with applications to multiple access channels and dead sensor diagnosis

Author

Listed:
  • Michael T. Goodrich

    (University of California)

  • Daniel S. Hirschberg

    (University of California)

Abstract

We study group-testing algorithms for resolving broadcast conflicts on a multiple access channel (MAC) and for identifying the dead sensors in a mobile ad hoc wireless network. In group-testing algorithms, we are asked to identify all the defective items in a set of items when we can test arbitrary subsets of items. In the standard group-testing problem, the result of a test is binary—the tested subset either contains defective items or not. In the more generalized versions we study in this paper, the result of each test is non-binary. For example, it may indicate whether the number of defective items contained in the tested subset is zero, one, or at least two. We give adaptive algorithms that are provably more efficient than previous group testing algorithms. We also show how our algorithms can be applied to solve conflict resolution on a MAC and dead sensor diagnosis. Dead sensor diagnosis poses an interesting challenge compared to MAC resolution, because dead sensors are not locally detectable, nor are they themselves active participants.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:15:y:2008:i:1:d:10.1007_s10878-007-9087-z
    DOI: 10.1007/s10878-007-9087-z
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    Cited by:

    1. 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.
    2. 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.
    3. Yongxi Cheng & Jue Guo & Feifeng Zheng, 2015. "A new randomized algorithm for group testing with unknown number of defective items," Journal of Combinatorial Optimization, Springer, vol. 30(1), pages 150-159, July.

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