On disjoint paths in acyclic planar graphs

We give an algorithm with complexity O(f(R) 2 kn) for the integer multiflow problem on instances (G,H, r, c) with G an acyclic planar digraph and r + c Eulerian. Here, f is a polynomial function, n = |V (G)|, k = |E(H)| and R is the maximum request maxh∈E(H) r(h). When k is fixed, this gives a polynomial algorithm for the arc-disjoint paths problem under the same hypothesis.