Mobile agent rendezvous in the ring

The mobile agent rendezvous problem is a search optimization problem based on the following question. How should k ≥ 2 mobile agents move along the n nodes of a network in order to minimize the time required to meet or rendezvous? In the asymmetric case of the problem, the mobile agents are uniquely identified and they can be assigned distinct algorithms in order to achieve a rendezvous. If the mobile agents cannot be distinguished, however, then they must run the same algorithm in an attempt to rendezvous. In the pure symmetric case of the rendezvous search problem, the mobile agents run the same deterministic algorithm while in the mixed symmetric case, they run the same randomized algorithm. When the rendezvous search problem is sufficiently symmetric, e.g., the mobile agents are identical, they have no common orientation, and the network is anonymous, rendezvous is impossible unless the symmetry is broken. Traditionally, the symmetry has been broken with randomization and thus almost all instances of the rendezvous search problem with significant symmetry are solved as mixed symmetric cases. We want to explore how rendezvous can occur in the pure symmetric cases of the rendezvous search problem. Since the mobile agents are executing the same deterministic algorithm, the symmetry in the problem must be broken by means other than randomization. We investigate how mobile agents can use identical tokens to break symmetry and thus rendezvous in the pure symmetric case. We are especially interested in the time and memory tradeoffs that such solutions make possible.