# The minimal spanning tree and the upper box dimension

##
Zvi Lotker

### projet Mascotte

### Résumé:

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