Skip to main content
Article thumbnail
Location of Repository

Rendezvous in higher dimensions

By Steven Alpern and Vic Baston


Two players are placed on the integer lattice Zn (consisting of points in n - dimensional space with all coordinates integers) so that their vector difference is of length 2 and parallel to one of the axes. Their aim is to move to an adjacent node in each period, so that they meet (occupy same node) in least expected time R (n) , called the Rendezvous Value. We assume they have no common notion of directions or orientations (i.e., no common notion of ‘clockwise’). We extend the known result R (1) = 3.25 of Alpern and Gal to obtain R (2) = 197/32 = 6. 16, and the bounds 2n ≤ R (n) ≤ ¡32n3 + 12n2 − 2n − 3¢/12n2. For n = 2 we characterize the set of all optimal strategies and show that none of them simultaneously maximize the probability of meeting by time t for all t. This behaviour differs from that found by Anderson and Fekete, and the authors, for the related problem where the players are initially placed at diagonals of one of the squares of the lattice Z2

Topics: QA Mathematics
Publisher: Centre for Discrete and Applicable Mathematics, London School of Economics and Political Science
Year: 2004
OAI identifier:
Provided by: LSE Research Online
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • (external link)
  • (external link)
  • Suggested articles

    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.