Finding Disjoint Paths on Directed Acyclic Graphs

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

Abstract

Given k + 1 pairs of vertices (s1,s2),(u1,v1),...,(uk,vk) of a directed acyclic graph, we show that a modified version of a data structure of Suurballe and Tarjan can output, for each pair (ul,vl) with 1 ≤ lk, a tuple (s1,t1,s2,t2) with {t1,t2} = {ul,vl} in constant time such that there are two disjoint paths p1, from s1 to t1, and p2, from s2 to t2, 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/nn) + nlog3n). In this problem, given a tuple (s1,s2,t1,t2) of four vertices, we want to construct two disjoint paths p1, from s1 to t1, and p2, from s2 to t2, 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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