{"title":"Integer Multiflows in Acyclic Planar Digraphs","authors":"Guyslain Naves","doi":"10.1007/s00493-023-00065-0","DOIUrl":null,"url":null,"abstract":"<p>We give an algorithm with complexity <span>\\(O((R+1)^{4k^2} k^3 n)\\)</span> for the integer multiflow problem on instances (<i>G</i>, <i>H</i>, <i>r</i>, <i>c</i>) with <i>G</i> an acyclic planar digraph and <span>\\(r+c\\)</span> Eulerian. Here, <span>\\(n = |V(G)|\\)</span>, <span>\\(k = |E(H)|\\)</span> and <i>R</i> is the maximum request <span>\\(\\max _{h \\in E(H)} r(h)\\)</span>. When <i>k</i> 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\nJournal 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:\nLaboratoire d'Informatique & Systèmes, Aix-Marseille Université, CNRS UMR 7020, Marseille, France</p>","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"13 3","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2023-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Combinatorica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00493-023-00065-0","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
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
针对实例（G，H，R，c）上的整数多流问题，给出了一个复杂度为O（（（R+1）^｛4k^2｝k^3n）的算法，其中G是非循环平面有向图和（R+c）Eulerian。这里，\（n=|V（G）|\），\（k=|E（H）|\。当k是固定的时，这给出了在相同假设下求解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的编辑。ConfirmedJournal指令要求加入城市和国家；然而，这些在隶属关系中是缺失的[1]。请核实所提供的城市是否正确，并在必要时进行修改。提交后，我的隶属关系发生了变化。现在应该是：信息实验室；法国马赛艾克斯马赛大学，CNRS UMR 7020
期刊介绍：
COMBINATORICA publishes research papers in English in a variety of areas of combinatorics and the theory of computing, with particular emphasis on general techniques and unifying principles. Typical but not exclusive topics covered by COMBINATORICA are
- Combinatorial structures (graphs, hypergraphs, matroids, designs, permutation groups).
- Combinatorial optimization.
- Combinatorial aspects of geometry and number theory.
- Algorithms in combinatorics and related fields.
- Computational complexity theory.
- Randomization and explicit construction in combinatorics and algorithms.
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