The power of tokens: rendezvous and symmetry detection for two mobile agents in a ring

Authors:
Jurek Czyzowicz;Stefan Dobrev;Evangelos Kranakis;Danny Krizanc
Affiliations:
Département d'informatique, Université du Québec en Outaouais, Gatineau, Québec, Canada;School of Information Technology and Engineering, University of Ottawa, Ottawa, Canada;School of Computer Science, Carleton University, Ottawa, Ontario, Canada;Department of Mathematics, Wesleyan University, Connecticut
Venue:
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
Year:
2008

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Abstract

Rendezvous with detection differs from the usual rendezvous problem in that two mobile agents not only accomplish rendezvous whenever this is possible, but can also detect the impossibility of rendezvous (e.g., due to symmetrical initial positions of the agents) in which case they are able to halt.We study the problem of rendezvous with and without detection of two anonymous mobile agents in a synchronous ring. The agents have constant memory and each of them possess one or more tokens which may be left at some nodes of the ring and noticed later. We derive sharp bounds for the case of at most two tokens per agent and also explore trade-offs between the number of tokens available to the agents and the time needed to accomplish rendezvous with detection.