Centre for Discrete and Applicable Mathematics

 CDAM Research Report, LSE-CDAM-2001-05

October 2001

Rendezvous in One and More Dimensions

Steve Alpern


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.

A PDF file (187 kB) with the full contents of this report can be downloaded by clicking here.

Alternatively, if you would like to get a free hard copy of this report, please send the number of this report, LSE-CDAM-2001-05, together with your name and postal address to:
CDAM Research Reports Series
Centre for Discrete and Applicable Mathematics
London School of Economics
Houghton Street
London WC2A 2AE, U.K.
Phone: +44(0)-20-7955 7732.
Fax: +44(0)-20-7955 6877.
Email: info@maths.lse.ac.uk

Introduction to the CDAM Research Report Series.
CDAM Homepage.

Copyright © London School of Economics & Political Science 2005

Last changed: Wed 9 Feb 2005
For comments go to: http://www.maths.lse.ac.uk/webmaster.html