O. Aichholzer, T. Hackl, M. Korman, A. Pilz, G. Rote, A. van Renssen,
M. Roeloffzen, and B. Vogtenhuber
Given a set of points in the plane, we want to establish a connection network
between these points that consists of several disjoint layers. Motivated by
sensor networks, we want that each layer is spanning and plane, and that no
edge is very long (when compared to the minimum length needed to obtain a
spanning graph). We consider two different approaches: first we show an
almost optimal centralized approach to extract two graphs. Then we show a
constant factor approximation for a distributed model in which each point can
compute its adjacencies using only local information. In both cases the
obtained layers are plane.