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Matching Points with Circles and Squares

  • Bernardo M. Ábrego
  • Esther M. Arkin
  • Silvia Fernández-Merchant
  • Ferran Hurtado
  • Mikio Kano
  • Joseph S. B. Mitchell
  • Jorge Urrutia
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3742)

Abstract

Given a class \({\mathcal C}\) of geometric objects and a point set P, a \({\mathcal C}\)-matching of P is a set M = {C 1, ...,C k } of elements of \({\mathcal C}\) such that each C i contains exactly two elements of P. If all of the elements of P belong to some C i , M is called a perfect matching; if in addition all the elements of M are pairwise disjoint we say that this matching M is strong. In this paper we study the existence and properties of \({\mathcal C}\)-matchings for point sets in the plane when \({\mathcal C}\) is the set of circles or the set of isothetic squares in the plane.

Keywords

Perfect Match Pairwise Disjoint Delaunay Triangulation Geometric Object Hamiltonian Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Czyzowicz, J., Rivera-Campo, E., Urrutia, J., Zaks, J.: Guarding rectangular art galleries. Discrete Mathematics 50, 149–157 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Dillencourt, M.: Toughness and Delaunay Triangulations. Discrete and Computational Geometry 5(6), 575–601 (1990); Preliminary version in Proc. of the 3rd Annual Symposium on Computational Geometry, Waterloo, pp. 186–194 (1987)Google Scholar
  3. 3.
    Liotta, G., Lubiw, A., Meijer, H., Whitesides, S.H.: The Rectangle of Influence Drawability Problem. Discrete and Computational Geometry 5(6), 575–601 (1990)MathSciNetGoogle Scholar
  4. 4.
    Pach, J. (ed.): Towards a Theory of Geometric Graphs, Amer. Math. Soc., Contemp. Math. Series, p. 342 (2004)Google Scholar
  5. 5.
    Preparata, F.P., Shamos, M.I.: Computational Geometry. An Introduction. Springer, Heidelberg (1995)Google Scholar
  6. 6.
    Sharir, M.: On k-Sets in Arrangements of Curves and Surfaces. Discrete and Computational Geometry 6, 593–613 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Tutte, W.T.: A theorem on planar graphs. Trans. Amer. Math. Soc. 82, 99–116 (1956)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Bernardo M. Ábrego
    • 1
  • Esther M. Arkin
    • 2
  • Silvia Fernández-Merchant
    • 1
  • Ferran Hurtado
    • 3
  • Mikio Kano
    • 4
  • Joseph S. B. Mitchell
    • 2
  • Jorge Urrutia
    • 5
  1. 1.Department of MathematicsCalifornia State UniversityNorthridge
  2. 2.Department of Applied Mathematics and StatisticsState University of New York at Stony Brook 
  3. 3.Departament de Matemàtica Aplicada IIUniversitat Politècnica de Catalunya 
  4. 4.Ibaraki University 
  5. 5.Instituto de MatemáticasUniversidad Nacional Autónoma de México 

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