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Issue No.07  July (2012 vol.11)
pp: 11401150
Jonathan P. Jenkins , North Carolina State University, Raleigh
Iyad A. Kanj , Lafayette College, Easton
Ge Xia , North Carolina State University, Raleigh
Fenghui Zhang , DePaul University, Chicago and Google, Kirkland
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TMC.2011.142
ABSTRACT
In this paper, we present local distributed algorithms for constructing spanners in wireless sensor networks modeled as unit ball graphs (shortly UBGs) and quasiunit ball graphs (shortly quasiUBGs), in the 3D euclidean space. Our first contribution is a local distributed algorithm that, given a UBG U and a parameter \alpha < \pi/3, constructs a sparse spanner of U with stretch factor 1/(12\sin {(\alpha/2)}), improving the previous upper bound of 1/(1\alpha ) by Althöfer et al. which is applicable only when \alpha < 1/(1+2\sqrt{2}) < \pi/3. The second contribution of this paper is in presenting the first local distributed algorithm for the construction of boundeddegree lightweight spanners of UBGs and quasiUBGs. The simulation results we obtained show that, empirically, the weight and the stretch factor of the spanners, and the locality of the algorithms, are much better than the theoretical upper bounds proved in this paper.
INDEX TERMS
3D spanners, sparse spanners, lightweight spanners, local distributed algorithms.
CITATION
Jonathan P. Jenkins, Iyad A. Kanj, Ge Xia, Fenghui Zhang, "Local Construction of Spanners in the 3D Space", IEEE Transactions on Mobile Computing, vol.11, no. 7, pp. 11401150, July 2012, doi:10.1109/TMC.2011.142
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