Untangling a polygon

János Pach, Gábor Tardos

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

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((nlogn)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.

Original languageEnglish
Title of host publicationGraph Drawing - 9th International Symposium, GD 2001, Revised Papers
EditorsPetra Mutzel, Michael Junger, Sebastian Leipert
PublisherSpringer Verlag
Pages154-161
Number of pages8
ISBN (Print)3540433090, 9783540433095
DOIs
Publication statusPublished - 2002
Event9th International Symposium on Graph Drawing, GD 2001 - Vienna, Austria
Duration: Sep 23 2001Sep 26 2001

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2265 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other9th International Symposium on Graph Drawing, GD 2001
CountryAustria
CityVienna
Period9/23/019/26/01

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Pach, J., & Tardos, G. (2002). Untangling a polygon. In P. Mutzel, M. Junger, & S. Leipert (Eds.), Graph Drawing - 9th International Symposium, GD 2001, Revised Papers (pp. 154-161). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2265 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-45848-4_13