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Integer Multiflows in Acyclic Planar Digraphs

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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

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  1. Laboratoire d’Informatique Fondamentale de Marseille, CNRS UMR 7279, Aix-Marseille University, Marseille, France

    Guyslain Naves

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  1. Guyslain Naves
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Naves, G. Integer Multiflows in Acyclic Planar Digraphs. Combinatorica 43, 1031–1043 (2023). https://doi.org/10.1007/s00493-023-00065-0

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