How to cut pseudo-parabolas into segments

Hisao Tamaki, Takeshi Tokuyama

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

4 Citations (Scopus)

Abstract

Let Γ be a collection of unbounded x-monotone Jordan arcs intersecting at most twice each other, which we call pseudo-parabolas, since two axis parallel parabolas intersects at most twice. We investigate how to cut pseudo-parabolas into the minimum number of curve segments so that each pair of segments intersect at most once. We give an Ω(n4/3) lower bound and O(n5/3) upper bound. We give the same bounds for an arrangement of circles. Applying the upper bound, we give an O(n23/12) bound on the complexity of a level of pseudo-parabolas, and O(n11/6) bound on the complexity of a combinatorially concave chain of pseudo parabolas. We also give some upperbounds on the number of transitions of the minimum weight matroid base when the weight of each element changes as a quadratic function of a single parameter.

Original languageEnglish
Title of host publicationProceedings of the 11th Annual Symposium on Computational Geometry, SCG 1995
PublisherAssociation for Computing Machinery
Pages230-237
Number of pages8
ISBN (Electronic)0897917243
DOIs
Publication statusPublished - 1995 Sep 1
Event11th Annual Symposium on Computational Geometry, SCG 1995 - Vancouver, Canada
Duration: 1995 Jun 51995 Jun 7

Publication series

NameProceedings of the Annual Symposium on Computational Geometry
VolumePart F129372

Other

Other11th Annual Symposium on Computational Geometry, SCG 1995
CountryCanada
CityVancouver
Period95/6/595/6/7

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Mathematics

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  • Cite this

    Tamaki, H., & Tokuyama, T. (1995). How to cut pseudo-parabolas into segments. In Proceedings of the 11th Annual Symposium on Computational Geometry, SCG 1995 (pp. 230-237). (Proceedings of the Annual Symposium on Computational Geometry; Vol. Part F129372). Association for Computing Machinery. https://doi.org/10.1145/220279.220304