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Let $G$ be a directed planar graph of complexity $n$, each arc having anonnegative 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 verticesincident with $t$. We give an algorithm to compute $k$ pairwise vertex-disjointpaths connecting the pairs $(s_i,t_i)$ in $G$, with minimal total length, in$O(kn\log n)$ time.

Shortest Vertex-Disjoint Two-Face Paths in Planar Graphs