20060414
Asynchronous deterministic rendezvous in graphs
Publication
Publication
Theoretical Computer Science , Volume 355  Issue 3 p. 315 326
Two mobile agents (robots) having distinct labels and located in nodes of an unknown anonymous connected graph have to meet. We consider the asynchronous version of this wellstudied rendezvous problem and we seek fast deterministic algorithms for it. Since in the asynchronous setting, meeting at a node, which is normally required in rendezvous, is in general impossible, we relax the demand by allowing meeting of the agents inside an edge as well. The measure of performance of a rendezvous algorithm is its cost: for a given initial location of agents in a graph, this is the number of edge traversals of both agents until rendezvous is achieved. If agents are initially situated at a distance D in an infinite line, we show a rendezvous algorithm with cost O(DLmin2) when D is known and O((D+Lmax)3) if D is unknown, where Lmin and Lmax are the lengths of the shorter and longer label of the agents, respectively. These results still hold for the case of the ring of unknown size, but then we also give an optimal algorithm of cost O(nLmin), if the size n of the ring is known, and of cost O(nLmax), if it is unknown. For arbitrary graphs, we show that rendezvous is feasible if an upper bound on the size of the graph is known and we give an optimal algorithm of cost O(DLmin) if the topology of the graph and the initial positions are known to agents.
Additional Metadata  

Asynchronous, Deterministic, Graph, Rendezvous  
dx.doi.org/10.1016/j.tcs.2005.12.016  
Theoretical Computer Science  
Organisation  School of Computer Science 
De Marco, G. (Gianluca), Gargano, L. (Luisa), Kranakis, E, Krizanc, D. (Danny), Pelc, A. (Andrzej), & Vaccaro, U. (Ugo). (2006). Asynchronous deterministic rendezvous in graphs. Theoretical Computer Science, 355(3), 315–326. doi:10.1016/j.tcs.2005.12.016
