Combinatorial complexity of signed discs

Extended abstract
  • Diane L. Souvaine
  • Chee-Keng Yap
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 709)


Let C+ and C be two collections of topological discs of arbitrary radii. 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 pC+¦, qC¦ and n=p+q≥5. Moreover, this bound is achievable. We also show bounds that are stated as functions of p and q. These are less precise.


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  1. [1]
    H. Edelsbrunner, L. Guibas, and M. Sharir. The complexity and construction of many faces in arrangments of lines and of segments. Discrete and Computational Geometry, 5:161–196, 1990.Google Scholar
  2. [2]
    M. T. Goodrich and D. Kravets. Point set pattern matching, 1992. Preprint.Google Scholar
  3. [3]
    L. J. Guibas, M. Sharir, and S. Sifrony. On the general motion-planning problem with 2 degrees of freedom. Discrete and Computational Geometry, 4:491–521, 1989.Google Scholar
  4. [4]
    K. Kedem, R. Livne, J. Pach, and M. Sharir. On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles. Discrete and Computational Geometry, 1:59–71, 1986.Google Scholar
  5. [5]
    Diane Souvaine and Chee Yap. Combinatorial complexity of signed discs. DIMACS Technical Report 92-54, Center for Discrete Mathematics and Theoretical Computer Science, New Jersey, December 1992.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Diane L. Souvaine
    • 1
  • Chee-Keng Yap
    • 2
  1. 1.Dept. of Computer ScienceRutgers UniversityNew Brunswick
  2. 2.Dept. of Computer ScienceNew York UniversityNew York

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