# The minimal spanning tree and the upper box dimension

## Zvi Lotker

### 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

 [Zvi Lotker] [projet Mascotte]