  Let $G$ be a directed planar graph of complexity $n$, each arc having a
nonnegative length. Let $s$ and $t$ be two distinct faces of $G$; let
$s_1,...,s_k$ be vertices incident with $s$; let $t_1,...,t_k$ be vertices
incident with $t$. We give an algorithm to compute $k$ pairwise vertex-disjoint
paths connecting the pairs $(s_i,t_i)$ in $G$, with minimal total length, in
$O(kn\log n)$ time.
