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Pure Strategy Asymmetric Rendezvous on the Line with an Unknown Initial Distance

Author

Listed:
  • Steve Alpern

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

  • Anatole Beck

    (Department of Mathematics, London School of Economics, Houghton Street, London WC2A 2AE, United Kingdom and Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706)

Abstract

Suppose two blind agents with unit speed are placed a distance H apart on an infinite line, and faced in random directions. Their initial distance H is picked from a distribution F with finite mean (mu). We present a pair of rendezvous strategies which do not depend on the distribution F and ensure a meeting in expected time less than 5:514(mu). This improves the bound of 5:74(mu) given by Baston and Gal. Furthermore, the bound we give is best possible for strategies of our type.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:48:y:2000:i:3:p:498-501
    DOI: 10.1287/opre.48.3.498.12432
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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. 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.
    3. Shmuel Gal, 1999. "Rendezvous Search on the Line," Operations Research, INFORMS, vol. 47(6), pages 974-976, December.
    4. J. V. Howard, 1999. "Rendezvous Search on the Interval and the Circle," Operations Research, INFORMS, vol. 47(4), pages 550-558, August.
    Full references (including those not matched with items on IDEAS)

    Citations

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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. Vic Baston & Shmuel Gal, 2001. "Rendezvous search when marks are left at the starting points," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(8), pages 722-731, December.
    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. 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.
    5. Steve Alpern, 2002. "Rendezvous Search: A Personal Perspective," Operations Research, INFORMS, vol. 50(5), pages 772-795, October.
    6. 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.
    7. 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.

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