Untangling a polygon

János Pach, G. Tardos

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

1 Citation (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 publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages154-161
Number of pages8
Volume2265 LNCS
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)03029743
ISSN (Electronic)16113349

Other

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

Fingerprint

Polygon
Simple Polygon
Closed

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Pach, J., & Tardos, G. (2002). Untangling a polygon. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2265 LNCS, pp. 154-161). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2265 LNCS).

Untangling a polygon. / Pach, János; Tardos, G.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 2265 LNCS 2002. p. 154-161 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2265 LNCS).

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

Pach, J & Tardos, G 2002, Untangling a polygon. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 2265 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2265 LNCS, pp. 154-161, 9th International Symposium on Graph Drawing, GD 2001, Vienna, Austria, 9/23/01.
Pach J, Tardos G. Untangling a polygon. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 2265 LNCS. 2002. p. 154-161. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Pach, János ; Tardos, G. / Untangling a polygon. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 2265 LNCS 2002. pp. 154-161 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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