  We study the problem of computing geometric spanners for (additively)
weighted point sets. A weighted point set is a set of pairs $(p,r)$ where $p$
is a point in the plane and $r$ is a real number. The distance between two
points $(p_i,r_i)$ and $(p_j,r_j)$ is defined as $|p_ip_j|-r_i-r_j$. We show
that in the case where all $r_i$ are positive numbers and $|p_ip_j|\geq
r_i+r_j$ for all $i,j$ (in which case the points can be seen as
non-intersecting disks in the plane), a variant of the Yao graph is a
$(1+\epsilon)$-spanner that has a linear number of edges. We also show that the
Additively Weighted Delaunay graph (the face-dual of the Additively Weighted
Voronoi diagram) has constant spanning ratio. The straight line embedding of
the Additively Weighted Delaunay graph may not be a plane graph. We show how to
compute a plane embedding that also has a constant spanning ratio.
