This paper discusses techniques to improve aggregate power efficiency of a wireless network using the key concepts of Delaunay triangulations and sparse covers. A measure of the power efficiency of such networks is the mean rate of a word of data successfully arriving at its destination per the power used to support the network, i.e., the average number of bytes successfully transmitted per Joule of energy. The quick yet naive approach is to create a large covering tree with a greedy heuristic. An alternative approach is to use randomized sparse covers of an approximate Delaunay triangulation.
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