Distributed Computing

, Volume 17, Issue 4, pp 303–310

Constant-time distributed dominating set approximation

Article

DOI: 10.1007/s00446-004-0112-5

Cite this article as:
Kuhn, F. & Wattenhofer, R. Distrib. Comput. (2005) 17: 303. doi:10.1007/s00446-004-0112-5

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.

Copyright information

© Springer-Verlag Berlin/Heidelberg 2005

Authors and Affiliations

  1. 1.Computer Engineering and Networks LaboratoryETH ZürichZürichSwitzerland