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Rendezvous Search on the Labeled Line

Author

Listed:
  • Elizabeth J. Chester

    (Department of Mathematics, University of California, Berkeley, California 94720)

  • Reha H. Tütüncü

    (Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213)

Abstract

The rendezvous search problem is the problem of finding optimal search strategies for two people who are placed randomly on a known search region and want to meet each other in minimal expected time. We focus on initial location distributions that are centrally symmetric and nonincreasing as one moves away from the center, including the discretized and/or truncated Gaussian densities. When the search region is a discrete or a continuous interval, and the interval is labeled so that the searchers know their own location at all times, we prove that the optimal strategy for both searchers is to go directly to the center and wait there. The same result also holds for rendezvous search on the infinite line.

Suggested Citation

  • Elizabeth J. Chester & Reha H. Tütüncü, 2004. "Rendezvous Search on the Labeled Line," Operations Research, INFORMS, vol. 52(2), pages 330-334, April.
    • Handle: RePEc:inm:oropre:v:52:y:2004:i:2:p:330-334
    DOI: 10.1287/opre.1030.0085
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    References listed on IDEAS

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    1. J. V. Howard, 1999. "Rendezvous Search on the Interval and the Circle," Operations Research, INFORMS, vol. 47(4), pages 550-558, August.
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    Cited by:

    1. Leone, Pierre & Buwaya, Julia & Alpern, Steve, 2022. "Search-and-rescue rendezvous," European Journal of Operational Research, Elsevier, vol. 297(2), pages 579-591.
    2. 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.
    3. Pierre Leone & Steve Alpern, 2022. "A Symbolic Programming Approach to the Rendezvous Search Problem," SN Operations Research Forum, Springer, vol. 3(1), pages 1-29, March.
    4. J. V. Howard & Marco Timmer, 2013. "New results on rendezvous search on the interval," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(6), pages 454-467, September.
    5. Alpern, Steve, 2008. "Line-of-sight rendezvous," European Journal of Operational Research, Elsevier, vol. 188(3), pages 865-883, August.
    6. Steve Alpern, 2011. "Find-and-Fetch Search on a Tree," Operations Research, INFORMS, vol. 59(5), pages 1258-1268, October.
    7. Cheng-Shang Chang & Wanjiun Liao & Ching-Min Lien, 2015. "On the Multichannel Rendezvous Problem: Fundamental Limits, Optimal Hopping Sequences, and Bounded Time-to-Rendezvous," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 1-23, February.
    8. Steve Alpern & Thomas Lidbetter, 2013. "Mining Coal or Finding Terrorists: The Expanding Search Paradigm," Operations Research, INFORMS, vol. 61(2), pages 265-279, April.
    9. Pierre Leone & Steve Alpern, 2018. "Rendezvous search with markers that can be dropped at chosen times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(6-7), pages 449-461, September.

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