  Given a graph G and k pairs of vertices (s_1,t_1), ..., (s_k,t_k), the
k-Vertex-Disjoint Paths problem asks for pairwise vertex-disjoint paths P_1,
..., P_k such that P_i goes from s_i to t_i. Schrijver [SICOMP'94] proved that
the k-Vertex-Disjoint Paths problem on planar directed graphs can be solved in
time n^{O(k)}. We give an algorithm with running time 2^{2^{O(k^2)}} n^{O(1)}
for the problem, that is, we show the fixed-parameter tractability of the
problem.
