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Discrete Search with Directional Information

Author

Listed:
  • Donald A. Berry

    (University of Minnesota, Minneapolis, Minnesota)

  • Roy F. Mensch

    (Prudential Insurance Company, Newark, New Jersey)

Abstract

An unknown number N of cells are arranged in numerical order. An object is hidden in cell N . The problem is to locate the object—thereby determining N —within n searches. We consider a version of this problem that has applications in several problem settings: locating flaws in a discrete circuit, locating nerve endings, or locating the end of a tree root. A search of a site determines whether a cell is present and contains the object, except that it might overlook, with known probability w , a cell that is present; that is, a cell can “wink.” A search of site i reveals an empty cell if i N ; the cell containing the object if i = N and the cell does not wink; and no cell if i > N or if i ≤ N and the cell winks. Various special cases are considered. We define “bisection strategies” and show that they are optimal when w = 0. When w > 0, we partially characterize optimal strategies when n = 2, and completely characterize optimal strategies when there are at most two cells. For various values of n and w we give tables of the probability of finding the object for three intuitively reasonable strategies.

Suggested Citation

  • Donald A. Berry & Roy F. Mensch, 1986. "Discrete Search with Directional Information," Operations Research, INFORMS, vol. 34(3), pages 470-477, June.
    • Handle: RePEc:inm:oropre:v:34:y:1986:i:3:p:470-477
    DOI: 10.1287/opre.34.3.470
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    Citations

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    Cited by:

    1. Hassin, Refael & Sarid, Anna, 2018. "Operations research applications of dichotomous search," European Journal of Operational Research, Elsevier, vol. 265(3), pages 795-812.
    2. Chun, Young H., 2016. "Designing repetitive screening procedures with imperfect inspections: An empirical Bayes approach," European Journal of Operational Research, Elsevier, vol. 253(3), pages 639-647.
    3. Ferguson, Thomas S., 1996. "A problem of minimax estimation with directional information," Statistics & Probability Letters, Elsevier, vol. 26(3), pages 205-211, February.
    4. Duvocelle, Benoit & Flesch, János & Staudigl, Mathias & Vermeulen, Dries, 2022. "A competitive search game with a moving target," European Journal of Operational Research, Elsevier, vol. 303(2), pages 945-957.
    5. Garrec, Tristan & Scarsini, Marco, 2020. "Search for an immobile hider on a stochastic network," European Journal of Operational Research, Elsevier, vol. 283(2), pages 783-794.

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