Improved Algorithms for the 2-Vertex Disjoint Paths Problem

  • Given distinct vertices s_1, s_2, t_1, and t_2 the 2-vertex-disjoint paths problem consists in determining two vertex-disjoint paths p_1, from s_1 to t_1, and p_2, from s_2 to t_2, if such paths exist. As a first result we show that by using some kind of sparsification technique the previously best known time bound of O(n + m alpha(m, n)) can be reduced to O(m + n alpha(n, n)), where alpha denotes the inverse of the Ackermann function. Moreover, we extend the very practical and simple algorithm of Hagerup for solving the 2-vertex-disjoint-paths problem on 3-connected planar graphs to a practical linear time algorithm for the 2-VDPP on general planar graphs thereby avoiding the computation of planar embeddings or triconnected components.

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Author:Torsten Tholey
Frontdoor URL
Series (Serial Number):Reports / Technische Berichte der Fakultät für Angewandte Informatik der Universität Augsburg (2007-16)
Publishing Institution:Universität Augsburg
Release Date:2007/12/20
Institutes:Fakultät für Angewandte Informatik
Fakultät für Angewandte Informatik / Institut für Informatik
Dewey Decimal Classification:0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik