Local Algorithms for Dominating and Connected Dominating Sets of Unit Disk Graphs (2007)
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BibTeX
@MISC{Czyzowicz07localalgorithms,
author = {J. Czyzowicz and S. Dobrev and T. Fevens and H. González-aguilar and E. Kranakis and J. Opatrny and J. Urrutia},
title = {Local Algorithms for Dominating and Connected Dominating Sets of Unit Disk Graphs},
year = {2007}
}
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Abstract
Many protocols in distributed computing make use of dominating and connected dominating sets, for example for broadcasting and the computation of routing. Ad hoc networks impose an additional requirement that algorithms for the construction of such sets should be local in the sense that each node of the network should make decisions based only on the information obtained from nodes located a constant (independent of the size of the network) number of steps away from it. The focus of the present paper is on providing local, constant approximation, deterministic algorithms for the construction of dominating and connected dominating sets of a Unit Disk Graph (UDG) with location aware nodes (i.e., nodes that know their coordinates in the plane). The size of the constructed set, in the case of the dominating set, is shown to be 5 times the optimal, while for the connected dominating set 7.453 + ɛ the optimal, for any arbitrarily small ɛ> 0. These are the first local algorithms in the scientific literature whose time
