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Rendezvous Search: A Personal Perspective

Author

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  • Steve Alpern

    (Department of Mathematics, The London School of Economics, Houghton Street, London WC2A 2AE, United Kingdom)

Abstract

The rendezvous-search problem was posed by the author 25 years ago. In its basic form, it asks how two unit speed players can find each other in least expected time, when randomly placed in a known dark region. The problem received little attention until about 10 years ago. This article surveys the rapid progress that has been made since then, and also presents some new results.

Suggested Citation

  • Steve Alpern, 2002. "Rendezvous Search: A Personal Perspective," Operations Research, INFORMS, vol. 50(5), pages 772-795, October.
    • Handle: RePEc:inm:oropre:v:50:y:2002:i:5:p:772-795
    DOI: 10.1287/opre.50.5.772.363
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    References listed on IDEAS

    as
    1. Wei Shi Lim & Steve Alpern & Anatole Beck, 1997. "Rendezvous Search on the Line with More Than Two Players," Operations Research, INFORMS, vol. 45(3), pages 357-364, June.
    2. R. D. Foley & T. P. Hill & M. C. Spruill, 1991. "Linear search with bounded resources," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(4), pages 555-565, August.
    3. 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.
    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.
    5. Steve Alpern, 2002. "Rendezvous search on labeled networks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(3), pages 256-274, April.
    6. Sugden, Robert, 1995. "A Theory of Focal Points," Economic Journal, Royal Economic Society, vol. 105(430), pages 533-550, May.
    7. Steve Alpern & Anatole Beck, 1999. "Rendezvous Search on the Line with Limited Resources: Maximizing the Probability of Meeting," Operations Research, INFORMS, vol. 47(6), pages 849-861, December.
    8. Shmuel Gal, 1999. "Rendezvous Search on the Line," Operations Research, INFORMS, vol. 47(6), pages 974-976, December.
    9. J. V. Howard, 1999. "Rendezvous Search on the Interval and the Circle," Operations Research, INFORMS, vol. 47(4), pages 550-558, August.
    10. Edward J. Anderson & Sándor P. Fekete, 2001. "Two Dimensional Rendezvous Search," Operations Research, INFORMS, vol. 49(1), pages 107-118, February.
    11. Alpern, Steve & Beck, Anatole, 1997. "Rendezvous search on the line with bounded resources: expected time minimization," European Journal of Operational Research, Elsevier, vol. 101(3), pages 588-597, September.
    12. Stanley J. Benkoski & Michael G. Monticino & James R. Weisinger, 1991. "A survey of the search theory literature," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(4), pages 469-494, August.
    13. Crawford, Vincent P & Haller, Hans, 1990. "Learning How to Cooperate: Optimal Play in Repeated Coordination Games," Econometrica, Econometric Society, vol. 58(3), pages 571-595, May.
    14. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. 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.
    2. Steve Alpern, 2011. "Find-and-Fetch Search on a Tree," Operations Research, INFORMS, vol. 59(5), pages 1258-1268, October.
    3. 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.
    4. Andreas Blume & April Mitchell Franco & Paul Heidhues, 2021. "Dynamic coordination via organizational routines," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(4), pages 1001-1047, November.
    5. Blume, Andreas, 2018. "Failure of common knowledge of language in common-interest communication games," Games and Economic Behavior, Elsevier, vol. 109(C), pages 132-155.
    6. Steve Alpern & Thomas Lidbetter, 2014. "Searching a Variable Speed Network," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 697-711, August.
    7. Steve Alpern, 2017. "Hide-and-Seek Games on a Network, Using Combinatorial Search Paths," Operations Research, INFORMS, vol. 65(5), pages 1207-1214, October.
    8. 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.
    9. Leone, Pierre & Buwaya, Julia & Alpern, Steve, 2022. "Search-and-rescue rendezvous," European Journal of Operational Research, Elsevier, vol. 297(2), pages 579-591.
    10. Richard Weber, 2012. "Optimal Symmetric Rendezvous Search on Three Locations," Mathematics of Operations Research, INFORMS, vol. 37(1), pages 111-122, February.
    11. 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.
    12. Steve Alpern & Thomas Lidbetter, 2013. "Mining Coal or Finding Terrorists: The Expanding Search Paradigm," Operations Research, INFORMS, vol. 61(2), pages 265-279, April.
    13. Oléron Evans, Thomas P. & Bishop, Steven R., 2013. "Static search games played over graphs and general metric spaces," European Journal of Operational Research, Elsevier, vol. 231(3), pages 667-689.
    14. Alpern, Steve, 2008. "Line-of-sight rendezvous," European Journal of Operational Research, Elsevier, vol. 188(3), pages 865-883, August.
    15. 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.
    16. Richard Weber, 2012. "Strategy for Quickest Second Meeting of Two Agents in Two Locations," Mathematics of Operations Research, INFORMS, vol. 37(1), pages 123-128, February.

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    2. 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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    5. Edward J. Anderson & Sándor P. Fekete, 2001. "Two Dimensional Rendezvous Search," Operations Research, INFORMS, vol. 49(1), pages 107-118, February.
    6. Steve Alpern & Anatole Beck, 1999. "Rendezvous Search on the Line with Limited Resources: Maximizing the Probability of Meeting," Operations Research, INFORMS, vol. 47(6), pages 849-861, December.
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    12. Steve Alpern, 2002. "Rendezvous search on labeled networks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(3), pages 256-274, April.
    13. 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.
    14. 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.
    15. 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.
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