Rendezvous of Mobile Agents in Directed Graphs

Abstract

Abstract. We study the problem of gathering at the same location two mobile agents that are dispersed in an unknown and unlabeled environment. This problem called Rendezvous, is a fundamental task in distributed coordination among autonomous entities. Most previous studies on the subject model the environment as an undirected graph and the solution techniques rely heavily on the fact that an agent can backtrack on any edge it traverses. However, such an assumption may not hold for certain scenarios, for instance a road network containing one-way streets. Thus, we consider the case of strongly connected directed graphs and present the first deterministic solution for rendezvous of two anonymous (identical) agents moving in such a digraph. Our algorithm achieves rendezvous with detection for any solvable instance of the problem, without any prior knowledge about the digraph, not even its size.

Deterministic Symmetric Rendezvous in Arbitrary Graphs: Overcoming Anonymity, Failures and Uncertainty

“…While all solutions studied here assume that the edges of the graph are bidirectional, some of the techniques could be extended to work for (strongly connected) directed graphs (e.g. see [11]). In general, solving rendezvous in directed graphs is more difficult due to the inability of agents to backtrack and this is one of directions for future research.…”

Rendezvous of Distance-Aware Mobile Agents in Unknown Graphs

“…In some papers, additional capacities are assumed for the agents to overcome other limitations, e.g. global vision is assumed to overcome memory limitations [15] or the capability to mark nodes using tokens [16] or whiteboards [5] is often used to break symmetry. The model used in this paper can be seen as a special case of the oracle model for computation [13] where the agent is allowed to query an oracle that has global knowledge of the environment.…”