非循环平面有向图中的整数多流

IF 1 2区数学 Q1 MATHEMATICS

Combinatorica Pub Date : 2023-09-19 DOI:10.1007/s00493-023-00065-0

Guyslain Naves

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引用次数: 0

摘要

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

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Integer Multiflows in Acyclic Planar Digraphs

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Integer Multiflows in Acyclic Planar Digraphs

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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来源期刊

Combinatorica 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

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.