Combinatorial complexity of signed discs

Diane L. Souvaine, Chee Yap

Research output: Contribution to journalArticle

Abstract

Let C+ and C- be two collections of topological discs. The collection of discs is 'topological' in the sense that their boundaries are Jordan curves and each pair of Jordan curves intersect at most twice. We prove that the region ∪C+ - ∪C- has combinatorial complexity at most 10n - 30 where p = |C+|, q = |C-| and n = p + q ≥ 5. Moreover, this bound is achievable. We also show less precise bounds that are stated as functions of p and q.

Original languageEnglish (US)
Pages (from-to)207-223
Number of pages17
JournalComputational Geometry: Theory and Applications
Volume5
Issue number4
DOIs
StatePublished - 1995

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Combinatorial Complexity
Jordan Curve
Signed
Intersect

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Computer Science Applications
  • Computational Mathematics
  • Control and Optimization
  • Geometry and Topology

Cite this

Combinatorial complexity of signed discs. / Souvaine, Diane L.; Yap, Chee.

In: Computational Geometry: Theory and Applications, Vol. 5, No. 4, 1995, p. 207-223.

Research output: Contribution to journalArticle

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