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

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

Abstract

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.

Keywords

Full Version Smooth Path Oriented Path High Path Shortcut Region 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© 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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