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Untangling a Polygon

  • János Pach
  • Gábor Tardos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2265)

Abstract

The following problem was raised by M. Watanabe. Let P be a self-intersecting closed polygon with n vertices in general position. How manys steps does it take to untangle P, i.e., to turn it into a simple polygon, if in each step we can arbitrarily relocate one of its vertices. It is shown that in some cases one has to move all but at most O((n log n)2/3) vertices. On the other hand, every polygon P can be untangled in at most n − Ω(√n) steps. Some related questions are also considered.

Keywords

Planar Graph Random Permutation Simple Polygon Closed Polygon Black Edge 
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.

References

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • János Pach
    • 1
  • Gábor Tardos
    • 1
  1. 1.Rényi Institute of MathematicsHungarian Academy of SciencesHungary

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