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Rendezvous on a Planar Lattice
Steve Alpern and Vic Baston
Vol. 53, No. 6 (Nov. - Dec., 2005), pp. 996-1006
Published by: INFORMS
Stable URL: http://www.jstor.org/stable/25146935
Page Count: 11
You can always find the topics here!Topics: Meetings, Optimal strategies, Operations research, Mathematical lattices, Coordinate systems, Search strategies, Left turns, Integers, Proximity searching
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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).
Operations Research © 2005 INFORMS