How to meet asynchronously (almost) everywhere

Two mobile agents (robots) with distinct labels have to meet in an arbitrary, possibly infinite, unknown connected graph or in an unknown connected terrain in the plane. Agents are modeled as points, and the route of each of them only depends on its label and on the unknown environment. The actual walk of each agent also depends on an asynchronous adversary that may arbitrarily vary the speed of the agent, stop it, or even move it back and forth, as long as the walk of the agent in each segment of its route is continuous, does not leave it and covers all of it. Meeting in a graph means that both agents must be at the same time in some node or in some point inside an edge of the graph, while meeting in a terrain means that both agents must be at the same time in some point of the terrain. Does there exist a deterministic algorithm that allows any two agents to meet in any unknown environment in spite of this very powerfull adversary? We give deterministic rendezvous algorithms for agen...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Jurek Czyzowicz, Arnaud Labourel, Andrzej Pelc
• Keywords: CORR 2010, Education, Mobile Agents, Unknown Connected Terrain, Unknown Environment