Optimal Memory Rendezvous of Anonymous Mobile Agents in a Unidirectional Ring

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 the non-symmetric 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 !(log logn) bits, see [15]. In this context we show an optimal algorithm that uses O(log k + log logn)-size internal memory and a single token available at each mobile agent which allows them to recognize the symmetric case efficiently. Note that both in the periodic as well as in the symmetric case the rendezvous cannot be completed by any deterministic procedure due to problems with breaking the symmetry.