On disjoint paths in acyclic planar graphs

Abstract

We give an algorithm with complexity $O(f(R{)}^{k^2}{k}^{3}n)$ 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 ${\max }_{h\in E(H)}r(h)$. When $k$ is fixed, this gives a polynomial algorithm for the arc-disjoint paths problem under the same hypothesis.