IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v60y2013i6p454-467.html
   My bibliography  Save this article

New results on rendezvous search on the interval

Author

Listed:
  • J. V. Howard
  • Marco Timmer

Abstract

In a rendezvous search problem, two players are placed in a network and must try to meet each other in the least possible expected time. We look at rendezvous search on a discrete interval in which the players are initially placed using independent draws (usually assumed to be from the same distribution). Some optimal solutions are known if this distribution is uniform, and also for certain other special types of distribution. In this article, we present two new results. First, we characterize the complete set of solutions for the uniform case, showing that all optimal strategies must have two specific properties (namely, of being swept and strictly geodesic). Second, we relate search strategies on the interval to proper binary trees, and use this correspondence to derive a recurrence relation for solutions to the symmetric rendezvous problem for any initial distribution. This relation allows us to solve any such problem computationally by dynamic programming. Finally, some ideas for future research are discussed. © Wiley Periodicals, Inc. Naval Research Logistics 60: 454–467, 2013

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:60:y:2013:i:6:p:454-467
    DOI: 10.1002/nav.21544
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.21544
    Download Restriction: no
    File URL: https://libkey.io/10.1002/nav.21544?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Steve Alpern, 2002. "Rendezvous search on labeled networks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(3), pages 256-274, April.
    2. J. V. Howard, 1999. "Rendezvous Search on the Interval and the Circle," Operations Research, INFORMS, vol. 47(4), pages 550-558, August.
    3. Elizabeth J. Chester & Reha H. Tütüncü, 2004. "Rendezvous Search on the Labeled Line," Operations Research, INFORMS, vol. 52(2), pages 330-334, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Leone, Pierre & Buwaya, Julia & Alpern, Steve, 2022. "Search-and-rescue rendezvous," European Journal of Operational Research, Elsevier, vol. 297(2), pages 579-591.
    3. 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.
    4. Alpern, Steve, 2008. "Line-of-sight rendezvous," European Journal of Operational Research, Elsevier, vol. 188(3), pages 865-883, August.
    5. Steve Alpern, 2011. "Find-and-Fetch Search on a Tree," Operations Research, INFORMS, vol. 59(5), pages 1258-1268, October.
    6. 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.
    7. 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.
    8. 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.
    9. Steve Alpern, 2002. "Rendezvous Search: A Personal Perspective," Operations Research, INFORMS, vol. 50(5), pages 772-795, October.
    10. Steve Alpern & Vic Baston, 2005. "Rendezvous on a Planar Lattice," Operations Research, INFORMS, vol. 53(6), pages 996-1006, December.
    11. Steve Alpern & Thomas Lidbetter, 2013. "Mining Coal or Finding Terrorists: The Expanding Search Paradigm," Operations Research, INFORMS, vol. 61(2), pages 265-279, April.
    12. Elizabeth J. Chester & Reha H. Tütüncü, 2004. "Rendezvous Search on the Labeled Line," Operations Research, INFORMS, vol. 52(2), pages 330-334, April.
    13. Alpern, Steve & Baston, Vic, 2006. "A common notion of clockwise can help in planar rendezvous," European Journal of Operational Research, Elsevier, vol. 175(2), pages 688-706, December.
    14. Edward J. Anderson & Sándor P. Fekete, 2001. "Two Dimensional Rendezvous Search," Operations Research, INFORMS, vol. 49(1), pages 107-118, February.
    15. Steve Alpern & Anatole Beck, 2000. "Pure Strategy Asymmetric Rendezvous on the Line with an Unknown Initial Distance," Operations Research, INFORMS, vol. 48(3), pages 498-501, June.
    16. Alpern, Steve & Katrantzi, Ioanna, 2009. "Equilibria of two-sided matching games with common preferences," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1214-1222, August.
    17. Steve Alpern, 2002. "Rendezvous search on labeled networks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(3), pages 256-274, April.
    18. Steve Alpern & Wei Shi Lim, 2002. "Rendezvous of three agents on the line," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(3), pages 244-255, April.
    19. Alpern, Steven & Lidbetter, Thomas, 2015. "Optimal trade-off between speed and acuity when searching for a small object," LSE Research Online Documents on Economics 61504, London School of Economics and Political Science, LSE Library.
    20. Steve Alpern, 2017. "Hide-and-Seek Games on a Network, Using Combinatorial Search Paths," Operations Research, INFORMS, vol. 65(5), pages 1207-1214, October.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:navres:v:60:y:2013:i:6:p:454-467. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.