Rendezvous of Mobile Agents without Agreement on Local Orientation

The exploration of a connected graph by multiple mobile agents has been previously studied under different conditions. A fundamental coordination problem in this context is the gathering of all agents at a single node, called the Rendezvous problem. To allow deterministic exploration, it is usually assumed that the edges incident to a node are locally ordered according to a fixed function called local orientation. We show that having a fixed local orientation is not necessary for solving rendezvous; Two or more agents having possibly distinct local orientation functions can rendezvous in all instances where rendezvous is solvable under a common local orientation function. This result is surprising and extends the known characterization of solvable instances for rendezvous and leader election in anonymous networks. On one hand, our model is more general than the anonymous port-to-port network model and on the other hand it is less powerful than qualitative model of Barrière et al. [4,9] where the agents have distinct labels. Our results hold even in the simplest model of communication using identical tokens and in fact, we show that using two tokens per agent is necessary and sufficient for solving the problem.