Optimal memory rendezvous of anonymous mobile agents in a unidirectional ring

Abstract

We study the rendezvous problem with k≥2 mobile agents in a n-node ring. We present a new algorithm which solves the rendezvous problem for any non-periodic distribution of agents on the ring. The mobile agents require the use of O(log k)-bit-wise size of internal memory and one indistinguishable token each. In the periodic (but not symmetric) case our new procedure allows the agents to conclude that rendezvous is not feasible. It is known that in the symmetric case the agents cannot decide the feasibility of rendezvous if their internal memory is limited to ω(log log n) bits, see [15]. In this context we show new space optimal deterministic algorithm allowing effective recognition of the symmetric case. The algorithm is based on O(log k + log log n)-bit internal memory and a single token provided to each mobile agent. Finally, it is known that both in the periodic as well as in the symmetric cases the rendezvous cannot be accomplished by any deterministic procedure due to problems with breaking symmetry. © Springer-Verlag Berlin Heidelberg 2006.