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Time versus space trade-offs for randezvous in trees

Abstract

Two identical (anonymous) mobile agents start from arbitrary nodes of an unknown tree and have to meet at some node. Agents move in synchronous rounds: in each round an agent can either stay at the current node or move to one of its neighbors. We consider deterministic algorithms for this rendezvous task. The main result of this paper is a tight trade-off between the optimal time of completing rendezvous and the size of memory of the agents. For agents with memory bits, we show that optimal rendezvous time is in -node trees. More precisely, if , for some constant , we design agents accomplishing rendezvous in arbitrary trees of size (unknown to the agents) in time , starting with arbitrary delay. We also show that no pair of agents can accomplish rendezvous in time , even in the class of lines of known length and even with simultaneous start. Finally, we prove that at least logarithmic memory is necessary for rendezvous, even for agents starting simultaneously in a -node line.

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Category:
Articles
Type:
artykuł w czasopiśmie wyróżnionym w JCR
Published in:
DISTRIBUTED COMPUTING no. 27, edition 2, pages 95 - 109,
ISSN: 0178-2770
Language:
English
Publication year:
2014
Bibliographic description:
Czyzowicz J., Kosowski A., Pelc A.: Time versus space trade-offs for randezvous in trees// DISTRIBUTED COMPUTING. -Vol. 27, iss. 2 (2014), s.95-109
Verified by:
Gdańsk University of Technology

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