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Rendezvous search on labeled networks

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  • Steve Alpern

Abstract

Two players are independently placed on a commonly labelled network X. They cannot see each other but wish to meet in least expected time. We consider continuous and discrete versions, in which they may move at unit speed or between adjacent distinct nodes, respectively. There are two versions of the problem (asymmetric or symmetric), depending on whether or not we allow the players to use different strategies. After obtaining some optimality conditions for general networks, we specialize to the interval and circle networks. In the first setting, we extend the work of J. V. Howard; in the second we prove a conjecture concerning the optimal symmetric strategy. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 256–274, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10011

Suggested Citation

  • Steve Alpern, 2002. "Rendezvous search on labeled networks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(3), pages 256-274, April.
    • Handle: RePEc:wly:navres:v:49:y:2002:i:3:p:256-274
    DOI: 10.1002/nav.10011
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    References listed on IDEAS

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    1. Steve Alpern & Anatole Beck, 1999. "Asymmetric Rendezvous on the Line Is a Double Linear Search Problem," Mathematics of Operations Research, INFORMS, vol. 24(3), pages 604-618, August.
    2. Shmuel Gal, 1999. "Rendezvous Search on the Line," Operations Research, INFORMS, vol. 47(6), pages 974-976, December.
    3. J. V. Howard, 1999. "Rendezvous Search on the Interval and the Circle," Operations Research, INFORMS, vol. 47(4), pages 550-558, August.
    4. Vic Baston, 1999. "Note: Two rendezvous search problems on the line," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(3), pages 335-340, April.
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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. 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.
    3. Steve Alpern, 2002. "Rendezvous Search: A Personal Perspective," Operations Research, INFORMS, vol. 50(5), pages 772-795, October.
    4. 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.
    5. Steve Alpern & Li Zeng, 2022. "Social Distancing, Gathering, Search Games: Mobile Agents on Simple Networks," Dynamic Games and Applications, Springer, vol. 12(1), pages 288-311, March.
    6. 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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