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Search for a Moving Element with the Minimum Total Cardinality of Tests

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Abstract

We consider the moving element search problem with the minimum total cardinality of tests. As a search space, we consider the set of integer points of a segment of length n. We prove that the total test cardinality of an asymptotically optimal adaptive strategy is \(n + 2\sqrt n \).

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References

  1. Aydinian, H., Cicalese, F., Deppe, C., and Lebedev, V., Optimal Strategies for a Model of Combinatorial Two-Sided Search, in Proc. 7th Int. Workshop on Optimal Codes and Related Topics (OC’2013), Albena, Bulgaria, Sept. 6–12, 2013, pp. 7–12.

  2. Aydinian, H., Cicalese, F., Deppe, C., and Lebedev, V., A Combinatorial Model of Two-Sided Search, Int. J. Found. Comput. Sci., 2018, vol. 29, no. 4, pp. 481–504.

    Article  MathSciNet  Google Scholar 

  3. Benkoski, S.J., Monticino, M.G., and Weisinger, J.R., A Survey of the Search Theory Literature, Naval Res. Logist., 1991, vol. 38, no. 4, pp. 469–494.

    Article  Google Scholar 

  4. Cicalese, F., Fault-Tolerant Search Algorithms, Berlin: Springer, 2013.

    Book  Google Scholar 

  5. Du, D.-Z. and Hwang, F.K., Combinatorial Group Testing and Its Applications, Singapore: World Sci., 2000, 2nd ed.

    MATH  Google Scholar 

  6. Koopman, B.O., Search and Screening, OEG Report, Washington, D.C.: Operations Evaluation Group, Office of the Chief of Naval Operations, Navy Dept., 1946, no. 56.

    Google Scholar 

  7. Ahlswede, R., Deppe, C., and Lebedev, V., Non-binary Error Correcting Codes with Noiseless Feedback, Localized Errors, or Both, Ann. European Acad. Sci., 2005, no. 1, pp. 285–309.

  8. Lebedev, V.S., Coding with Noiseless Feedback, Probl. Peredachi Inf., 2016, vol. 52, no. 2, pp. 3–14 [Probl. Inf. Transm. (Engl. Transl.), 2016, vol. 52, no. 2, pp. 103–113].

    MathSciNet  MATH  Google Scholar 

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Funding

The research was supported in part by the Russian Foundation for Basic Research, project no. 19-01-00364.

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Authors and Affiliations

  1. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

    A. V. Lebedev & V. S. Lebedev

Authors
  1. A. V. Lebedev
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  2. V. S. Lebedev
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Correspondence to A. V. Lebedev.

Additional information

Russian Text © The Author(s), 2019, published in Problemy Peredachi Informatsii, 2019, Vol. 55, No. 4, pp. 107–111.

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Lebedev, A.V., Lebedev, V.S. Search for a Moving Element with the Minimum Total Cardinality of Tests. Probl Inf Transm 55, 396–400 (2019). https://doi.org/10.1134/S0032946019040057

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  • DOI: https://doi.org/10.1134/S0032946019040057

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