Centre for Discrete and Applicable Mathematics 

CDAM Research Report, LSECDAM200621December 2006 
Two Conjectures on Rendezvous in K_{3}
Steve Alpern and Shmuel Gal
The symmetric rendezvous problem on the triangle K_{3} asks how two players, initially randomly placed at distinct vertices, can meet in the minimal expected number of steps v. They must follow a common mixed strategy, with independent randomization. This problem, posed by Alpern as the 'telephone problem' and first studied by Anderson and Weber, assumes they have no common notion of a clockwise direction around the triangle  if they do, then the resulting 'common clockwise' problem has a minimum meeting time w which cannot be larger than v. This short note relates two conjectures about this problem, and briefly discusses a similar result for the symmetric rendezvous problem on the line  with and without a common sense of direction.A PDF file (53 kB) with the full contents of this report can be downloaded by clicking here.
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