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

我们给出一个复杂度为\(O((R+1)^{4k^2} k^3 n)\) 的算法，用于解决实例 ( G ,  H ,  r ,  c )上的整数多流问题，其中G是无环平面有向图和\(r+c\)欧拉。这里，\(n = |V(G)|\)、\(k = |E(H)|\)且R是最大请求\(\max _{h \in E(H)} r(h )\)。当k是固定的，这给出了在相同假设下弧不相交路径问题的多项式时间算法。请检查并确认标题中所做的编辑。已确认的期刊指令需要城市和国家作为隶属关系；然而，这些在从属关系中缺失[1]。请验证所提供的城市是否正确，并在必要时进行修改。自提交以来，我的隶属关系发生了变化。现在应该是：Laboratoire d'Informatique & Systèmes, Aix-Marseille Université, CNRS UMR 7020, Marseille, France