Deterministic Rendezvous of Asynchronous Bounded-Memory Agents in Polygonal Terrains
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Two mobile agents, modeled as points starting at different locations of an unknown terrain, have to meet. The terrain is a polygon with polygonal holes. We consider two versions of this rendezvous problem: exact RV, when the points representing the agents have to coincide at some time, and ε-RV, when these points have to get at distance less than ε in the terrain. In any terrain, each agent chooses its trajectory, but the movements of the agent on this trajectory are controlled by an adversary that may, e.g., speed up or slow down the agent. Agents have bounded memory: their computational power is that of finite state machines. Our aim is to compare the feasibility of exact and of ε-RV when agents are anonymous vs. when they are labeled. We show classes of polygonal terrains which distinguish all the studied scenarios from the point of view of feasibility of rendezvous. The features which influence the feasibility of rendezvous include symmetries present in the terrains, boundedness of their diameter, and the number of vertices of polygons in the terrains.
KeywordsMobile agent Rendezvous Deterministic Polygon Obstacle Bounded memory
Research of J. Czyzowicz was partially supported by NSERC discovery grant. Work of A. Kosowski was done during this author’s visit at the Université du Québec en Outaouais and was partially supported by Polish Ministry Grant N206 491738. Research of A. Pelc was partially supported by NSERC discovery grant and by the Research Chair in Distributed Computing at the Université du Québec en Outaouais.
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