Combinatorial complexity of signed discs

Diane L. Souvaine, Chee Keng Yap

Research output: Contribution to journalArticlepeer-review


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
Issue number4
StatePublished - Nov 1995

ASJC Scopus subject areas

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


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