Selecting vertex disjoint paths in plane graphs

Holger Flier, Matús Mihalák*, Peter Widmayer, Anna Zych, Yusuke Kobayashi, Anita Schöbel

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


We study variants of the vertex disjoint paths problem in plane graphs where paths have to be selected from given sets of paths. We investigate the problem as a decision, maximization, and routing-in-rounds problem. Although all considered variants are np-hard in planar graphs, restrictions on the locations of the terminals on the outer face of the given planar embedding of the graph lead to polynomially solvable cases for the decision and maximization versions of the problem. For the routing-in-rounds problem, we obtain a p-approximation algorithm, where p is the maximum number of alternative paths for a terminal pair, when restricting the locations of the terminals to the outer face such that they appear in a counterclockwise traversal of the boundary as a sequence for some permutation.
Original languageEnglish
Pages (from-to)136-144
Number of pages9
Issue number2
Publication statusPublished - 2015

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