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- Publisher
- Springer Journals
- Copyright
- Copyright © 2005 by Springer-Verlag Berlin/Heidelberg
- Subject
- Computer Science; Computer Hardware; Computer Systems Organization and Communication Networks; Software Engineering/Programming and Operating Systems; Theory of Computation
- ISSN
- 0178-2770
- eISSN
- 1432-0452
- DOI
- 10.1007/s00446-004-0112-5
- Publisher site
- See Article on Publisher Site
Abstract
Finding a small dominating set is one of the most fundamental problems of classical graph theory. In this paper, we present a new fully distributed approximation algorithm based on LP relaxation techniques. For an arbitrary, possibly constant parameter k and maximum node degree $\Delta$ , our algorithm computes a dominating set of expected size ${\rm O}(k\Delta^{2/k}{\rm log}(\Delta)\vert DS_{\rm {OPT}}\vert)$ in ${\rm O}{(k^2)}$ rounds. Each node has to send ${\rm O}{(k^2\Delta)}$ messages of size ${\rm O}({\rm log}\Delta)$ . This is the first algorithm which achieves a non-trivial approximation ratio in a constant number of rounds.
Journal
Distributed Computing – Springer Journals
Published: Jan 1, 2004