Matching points with circles and squares

  • Authors:

  • Bernardo M. Ábrego;Esther M. Arkin;Silvia Fernández-Merchant;Ferran Hurtado;Mikio Kano;Joseph S. B. Mitchell;Jorge Urrutia

  • Affiliations:

  • Department of Mathematics, California State University, Northridge;Department of Applied Mathematics and Statistics, State University of New York at Stony Brook;Department of Mathematics, California State University, Northridge;Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya;Ibaraki University;Department of Applied Mathematics and Statistics, State University of New York at Stony Brook;Instituto de Matemáticas, Universidad Nacional Autónoma de México

  • Venue:
  • JCDCG'04 Proceedings of the 2004 Japanese conference on Discrete and Computational Geometry
  • Year:
  • 2004

  • Squares

    LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics

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Abstract

Given a class ${\mathcal C}$ of geometric objects and a point set P, a ${\mathcal C}$-matching of P is a set M = {C1, ...,Ck} of elements of ${\mathcal C}$ such that each Ci contains exactly two elements of P. If all of the elements of P belong to some Ci, 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.