Integer Multiflows in Acyclic Planar Digraphs

Abstract

We give an algorithm with complexity \(O((R+1)^{4k^2} k^3 n)\) for the integer multiflow problem on instances (G, H, r, c) with G an acyclic planar digraph and \(r+c\) Eulerian. Here, \(n = |V(G)|\), \(k = |E(H)|\) and R is the maximum request \(\max _{h \in E(H)} r(h)\). When k is fixed, this gives a polynomial-time algorithm for the arc-disjoint paths problem under the same hypothesis.Kindly check and confirm the edit made in the title.Confirmed Journal instruction requires a city and country for affiliations; however, these are missing in affiliation [1]. Please verify if the provided city is correct and amend if necessary.Since the submission, my affiliation has changed. It should now be: Laboratoire d'Informatique & Systèmes, Aix-Marseille Université, CNRS UMR 7020, Marseille, France