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Rendezvous on a Planar Lattice

Author

Listed:
  • Steve Alpern

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

  • Vic Baston

    (Department of Mathematics, University of Southampton, Southampton, Hampshire SO17 1BJ, United Kingdom)

Abstract

We analyze the optimal behavior of two players who are lost on a planar surface and who want to meet each other in least expected time. They each know the initial distribution of the other’s location, but have no common labeling of points, and so cannot simply go to a location agreed to in advance. They have no compasses, so do not even have a common notion of North. For simplicity, we restrict their motions to the integer lattice Z 2 (graph paper) and their motions to horizontal and vertical directions, as in the original work of Anderson and Fekete (2001).

Suggested Citation

  • Steve Alpern & Vic Baston, 2005. "Rendezvous on a Planar Lattice," Operations Research, INFORMS, vol. 53(6), pages 996-1006, December.
    • Handle: RePEc:inm:oropre:v:53:y:2005:i:6:p:996-1006
    DOI: 10.1287/opre.1050.0217
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    References listed on IDEAS

    as
    1. Shmuel Gal, 1999. "Rendezvous Search on the Line," Operations Research, INFORMS, vol. 47(6), pages 974-976, December.
    2. J. V. Howard, 1999. "Rendezvous Search on the Interval and the Circle," Operations Research, INFORMS, vol. 47(4), pages 550-558, August.
    3. Edward J. Anderson & Sándor P. Fekete, 2001. "Two Dimensional Rendezvous Search," Operations Research, INFORMS, vol. 49(1), pages 107-118, February.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    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. Kikuta, Kensaku & Ruckle, William H., 2010. "Two point one sided rendezvous," European Journal of Operational Research, Elsevier, vol. 207(1), pages 78-82, November.
    3. Alpern, Steve, 2008. "Line-of-sight rendezvous," European Journal of Operational Research, Elsevier, vol. 188(3), pages 865-883, August.
    4. 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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