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Optimal Trade-Off Between Speed and Acuity When Searching for a Small Object

Author

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  • Steve Alpern

    (Warwick Business School, University of Warwick, Coventry CV4 7AL, United Kingdom)

  • Thomas Lidbetter

    (Department of Management, London School of Economics, London WC2A 2AE, United Kingdom)

Abstract

A Searcher seeks to find a stationary Hider located at some point H (not necessarily a node) on a given network Q . The Searcher can move along the network from a given starting point at unit speed, but to actually find the Hider she must pass it while moving at a fixed slower speed (which may depend on the arc). In this “bimodal search game,” the payoff is the first time the Searcher passes the Hider while moving at her slow speed. This game models the search for a small or well hidden object (e.g., a contact lens, improvised explosive device, predator search for camouflaged prey). We define a bimodal Chinese postman tour as a tour of minimum time δ which traverses every point of every arc at least once in the slow mode. For trees and weakly Eulerian networks (networks containing a number of disjoint Eulerian cycles connected in a tree-like fashion) the value of the bimodal search game is δ /2. For trees, the optimal Hider strategy has full support on the network. This differs from traditional search games, where it is optimal for him to hide only at leaf nodes. We then consider the notion of a lucky Searcher who can also detect the Hider with a positive probability q even when passing him at her fast speed. This paper has particular importance for demining problems.

Suggested Citation

  • Steve Alpern & Thomas Lidbetter, 2015. "Optimal Trade-Off Between Speed and Acuity When Searching for a Small Object," Operations Research, INFORMS, vol. 63(1), pages 122-133, February.
    • Handle: RePEc:inm:oropre:v:63:y:2015:i:1:p:122-133
    DOI: 10.1287/opre.2014.1331
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    References listed on IDEAS

    as
    1. Steve Alpern & Thomas Lidbetter, 2013. "Mining Coal or Finding Terrorists: The Expanding Search Paradigm," Operations Research, INFORMS, vol. 61(2), pages 265-279, April.
    2. Steve Alpern, 2011. "A New Approach to Gal’s Theory of Search Games on Weakly Eulerian Networks," Dynamic Games and Applications, Springer, vol. 1(2), pages 209-219, June.
    3. Qiaoming Han & Donglei Du & Juan Vera & Luis F. Zuluaga, 2008. "Improved Bounds for the Symmetric Rendezvous Value on the Line," Operations Research, INFORMS, vol. 56(3), pages 772-782, June.
    4. Kensaku Kikuta & William H. Ruckle, 1994. "Initial point search on weighted trees," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(6), pages 821-831, October.
    5. Shmuel Gal, 1999. "Rendezvous Search on the Line," Operations Research, INFORMS, vol. 47(6), pages 974-976, December.
    6. J. V. Howard, 1999. "Rendezvous Search on the Interval and the Circle," Operations Research, INFORMS, vol. 47(4), pages 550-558, August.
    7. Reijnierse, J H & Potters, J A M, 1993. "Search Games with Immobile Hider," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(4), pages 385-394.
    8. Richard Weber, 2012. "Optimal Symmetric Rendezvous Search on Three Locations," Mathematics of Operations Research, INFORMS, vol. 37(1), pages 111-122, February.
    9. Ljiljana Pavlović, 1995. "A search game on the union of graphs with immobile hider," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(8), pages 1177-1189, December.
    10. Elizabeth J. Chester & Reha H. Tütüncü, 2004. "Rendezvous Search on the Labeled Line," Operations Research, INFORMS, vol. 52(2), pages 330-334, April.
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    Cited by:

    1. Steve Alpern, 2017. "Hide-and-Seek Games on a Network, Using Combinatorial Search Paths," Operations Research, INFORMS, vol. 65(5), pages 1207-1214, October.
    2. Yolmeh, Abdolmajid & Baykal-Gürsoy, Melike, 2021. "Weighted network search games with multiple hidden objects and multiple search teams," European Journal of Operational Research, Elsevier, vol. 289(1), pages 338-349.
    3. Jake Clarkson & Kevin D. Glazebrook & Kyle Y. Lin, 2020. "Fast or Slow: Search in Discrete Locations with Two Search Modes," Operations Research, INFORMS, vol. 68(2), pages 552-571, March.
    4. Lisa Hellerstein & Thomas Lidbetter & Daniel Pirutinsky, 2019. "Solving Zero-Sum Games Using Best-Response Oracles with Applications to Search Games," Operations Research, INFORMS, vol. 67(3), pages 731-743, May.
    5. Steve Alpern & Thomas Lidbetter, 2019. "Approximate solutions for expanding search games on general networks," Annals of Operations Research, Springer, vol. 275(2), pages 259-279, April.
    6. Lidbetter, Thomas, 2020. "Search and rescue in the face of uncertain threats," European Journal of Operational Research, Elsevier, vol. 285(3), pages 1153-1160.
    7. Alpern, Steve & Fokkink, Robbert & Simanjuntak, Martin, 2016. "Optimal search and ambush for a hider who can escape the search region," European Journal of Operational Research, Elsevier, vol. 251(3), pages 707-714.
    8. Baston, Vic & Kikuta, Kensaku, 2019. "A search problem on a bipartite network," European Journal of Operational Research, Elsevier, vol. 277(1), pages 227-237.
    9. 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.
    10. Lidbetter, Thomas, 2017. "On the approximation ratio of the Random Chinese Postman Tour for network search," European Journal of Operational Research, Elsevier, vol. 263(3), pages 782-788.

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