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We estimate the total energy necessary for broadcasts in sensor
networks located on a fractal terrain by showing a connection
between weighted Euclidean minimal spanning tree (EMST) and the
upper box dimension of the terrain. More precisely for a set of
points in a metric space with upper box dimension $d$, the
$\alpha$-weight of the EMST is bounded for every $\alpha>d$ and
unbounded for every $\alpha
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