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Finding Disjoint Paths on Directed Acyclic Graphs

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Graph-Theoretic Concepts in Computer Science (WG 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3787))

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Abstract

Given k + 1 pairs of vertices (s 1,s 2),(u 1,v 1),...,(u k ,v k ) of a directed acyclic graph, we show that a modified version of a data structure of Suurballe and Tarjan can output, for each pair (u l ,v l ) with 1 ≤ l≤ k, a tuple (s 1,t 1,s 2,t 2) with {t 1,t 2} = {u l ,v l } in constant time such that there are two disjoint paths p 1, from s 1 to t 1, and p 2, from s 2 to t 2, if such a tuple exists. Disjoint can mean vertex- as well as edge-disjoint. As an application we show that the presented data structure can be used to improve the previous best known running time O(mn) for the so called 2-disjoint paths problem on directed acyclic graphs to O(m(log2 + m/n n) + nlog3 n). In this problem, given a tuple (s 1,s 2,t 1,t 2) of four vertices, we want to construct two disjoint paths p 1, from s 1 to t 1, and p 2, from s 2 to t 2, if such paths exist.

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Authors and Affiliations

  1. Institut für Informatik, Universität Augsburg, D-86135, Augsburg, Germany

    Torsten Tholey

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  1. Torsten Tholey
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Editors and Affiliations

  1. LITA, Université Paul Verlaine-Metz, 57045, Metz Cedex 01, France

    Dieter Kratsch

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© 2005 Springer-Verlag Berlin Heidelberg

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Tholey, T. (2005). Finding Disjoint Paths on Directed Acyclic Graphs. In: Kratsch, D. (eds) Graph-Theoretic Concepts in Computer Science. WG 2005. Lecture Notes in Computer Science, vol 3787. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11604686_28

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  • DOI: https://doi.org/10.1007/11604686_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-31000-6

  • Online ISBN: 978-3-540-31468-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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