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Time vs. space trade-offs for rendezvous in trees

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Time vs. space trade-offs for rendezvous in trees

Content Provider	ACM Digital Library
Author	Pelc, Andrzej Czyzowicz, Jurek Kosowski, Adrian
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 k memory bits, we show that optimal rendezvous time is $Θ(n+n^{2}/k)$ in n-node trees. More precisely, if k ≥ c log n, for some constant c, we design agents accomplishing rendezvous in arbitrary trees of unknown size n in time $O(n+n^{2/k}),$ starting with arbitrary delay. We also show that no pair of agents can accomplish rendezvous in time $o(n+n^{2}/k),$ 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 n-node line.
Starting Page	1
Ending Page	10
Page Count	10
File Format	PDF
ISBN	9781450312134
DOI	10.1145/2312005.2312007
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2012-06-25
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Memory space Time Rendezvous Anonymous agents
Content Type	Text
Resource Type	Article

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3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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