Centre for Discrete and Applicable Mathematics

 CDAM Research Report, LSE-CDAM-2001-05

October 2001


Rendezvous in One and More Dimensions

Steve Alpern

Abstract

This article is mainly concerned with the rendezvous problem on the n-dimensional integer lattice. Two blind players are initially placed at nodes whose difference vector has length 2 and is parallel to some coordinate axis. In each period they must move to an adjacent node. They have no common notion of locations or directions. The least expected rendezvous times R a (using distinct strategies) and R s (using the same mixed strategy) are shown to satisfy lim R a(n) = n  8/3 and lim R s(n) = n  56/9. This work extends the work of the author and S. Gal (R a(1) = 13/4) and that of V. Baston (R s(1)  4.5), and the related 2-dimensional analysis of Anderson and Fekete. We also consider a rendezvous problem on the line where one player can see the other.


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