Finding Disjoint Paths on Directed Acyclic Graphs

  • Torsten Tholey
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3787)


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 ≤ lk, 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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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Torsten Tholey
    • 1
  1. 1.Institut für InformatikUniversität AugsburgAugsburgGermany

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