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Rendezvous on a Planar Lattice

Steve Alpern and Vic Baston
Operations Research
Vol. 53, No. 6 (Nov. - Dec., 2005), pp. 996-1006
Published by: INFORMS
Stable URL: http://www.jstor.org/stable/25146935
Page Count: 11
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Rendezvous on a Planar Lattice
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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 Z² (graph paper) and their motions to horizontal and vertical directions, as in the original work of Anderson and Fekete (2001).

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