Issue No. 04 - April (2009 vol. 8)

ISSN: 1536-1233

pp: 460-474

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TMC.2008.132

Ge Xia , Lafayette College, Easton

Ljubomir Perković , DePaul University, Chicago

Iyad A. Kanj , DePaul University, Chicago

ABSTRACT

We present a local distributed algorithm that, given a wireless ad hoc network modeled as a unit disk graph U in the plane, constructs a planar power spanner of U whose degree is bounded by k and whose stretch factor is bounded by 1 + (2\sin{\frac{\pi}{k}})^{p}, where k \geq 10 is an integer parameter and p \in [2, 5] is the power exponent constant. For the same degree bound k, the stretch factor of our algorithm significantly improves the previous best bounds by Song et al. We show that this bound is near-optimal by proving that the slightly smaller stretch factor of 1 + (2\sin{\frac{\pi}{k + 1}})^{p} is unattainable for the same degree bound k. In contrast to previous algorithms for the problem, the presented algorithm is local. As a consequence, the algorithm is highly scalable and robust. Finally, while the algorithm is efficient and easy to implement in practice, it relies on deep insights on the geometry of unit disk graphs and novel techniques that are of independent interest.

INDEX TERMS

Spanners, unit disk graphs, Gabriel graphs, Yao graphs, local distributed algorithms.

CITATION

Ge Xia, Ljubomir Perković, Iyad A. Kanj, "Local Construction of Near-Optimal Power Spanners for Wireless Ad Hoc Networks",

*IEEE Transactions on Mobile Computing*, vol. 8, no. , pp. 460-474, April 2009, doi:10.1109/TMC.2008.132