Homotopic \(\mathcal{C}\)-Oriented Routing

  • Kevin Verbeek
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7704)


We study the problem of finding non-crossing minimum-link \(\mathcal{C}\)-oriented  paths that are homotopic to a set of input paths in an environment with \(\mathcal{C}\)-oriented obstacles. We introduce a special type of \(\mathcal{C}\)-oriented paths—smooth paths—and present a 2-approximation algorithm that runs in O(n 2 (n + logκ) + k in logn) time, where n is the total number of paths and obstacle vertices, k in is the total number of links in the input, and \(\kappa = |\mathcal{C}|\). The algorithm also computes an O(κ)-approximation for general \(\mathcal{C}\)-oriented paths. As a related result we show that, given a set of \(\mathcal{C}\)-oriented paths with L links in total, non-crossing \(\mathcal{C}\)-oriented paths homotopic to the input paths can require a total of Ω(L logκ) links.


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Kevin Verbeek
    • 1
  1. 1.Dep. of Mathematics and Computer ScienceTU EindhovenThe Netherlands

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