  In the semi-discrete version of Monge's problem one tries to find a transport
map $T$ with minimum cost from an absolutely continuous measure $\mu$ on
$\mathbb{R}^d$ to a discrete measure $\nu$ that is supported on a finite set in
$\mathbb{R}^d$.
  The problem is considered for the case of the Euclidean cost function.
Existence and uniqueness is shown by an explicit construction which yields a
one-to-one mapping between the optimal $T$ and an additively weighted Voronoi
partition of $\mathbb{R}^d$. From the proof an algorithm is derived to compute
this partition.
