Randomized Rendezvous Algorithms for Agents on a Ring with Different Speeds
Evangelos Kranakis, Danny Kriz̧anc, Fraser MacQuarrie, Sunil M. Shende · 2015
We provide randomized rendezvous algorithms for two synchronous robots in a bi-directional ring of length n (n is a real number): the robots are equipped with identical chronometers, execute identical algorithms, but have different speeds u, 1 (where u > 1). In general, neither of the robots are aware of their own speed but in some cases they may be aware either of the magnitude of u or some quantity of time that depends on u, n. The robots start by choosing a direction uniformly and independently at random. Given integer k ≥ 0, we design algorithms that have the two robots alternate for k + 1 rounds between choosing the direction at random followed by walking for a predetermined time. In the last round the robots walk until rendezvous.