Centre for Discrete and Applicable Mathematics

CDAM Research Report, LSE-CDAM-2006-21

December 2006

Two Conjectures on Rendezvous in K₃

Steve Alpern and Shmuel Gal

The symmetric rendezvous problem on the triangle K₃ 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.

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		Phone: +44(0)-20-7955 7494. Fax: +44(0)-20-7955 6877. Email: info@maths.lse.ac.uk