Separability by two lines and by nearly straight polygonal chains

  • Authors:
  • Ferran Hurtado;Mercè Mora;Pedro A. Ramos;Carlos Seara

  • Affiliations:
  • Departament de Matemítica Aplicada II, Universitat Politècnica de Catalunya, Pau Gargallo 5, E-08028 Barcelona, Spain;Departament de Matemítica Aplicada II, Universitat Politècnica de Catalunya, Pau Gargallo 5, E-08028 Barcelona, Spain;Departamento de Matemáticas, Universidad de Alcalá, Aptdo. de Correos 20, 28871 Alcalá de Henares, Madrid, Spain;Departament de Matemítica Aplicada II, Universitat Politècnica de Catalunya, Pau Gargallo 5, E-08028 Barcelona, Spain

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2004

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Abstract

In this paper, we study the separability in the plane by two criteria: double-wedge separability and @Q-separability. We give an O(NlogN)-time optimal algorithm for computing all the vertices of separating double wedges of two disjoint sets of objects (points, segments, polygons and circles) and an O((N/@Q"0)logN)-time algorithm for computing a nearly straight minimal @Q-polygonal chain separating two sets of points, where @Q"0 is a value which depends on the position of the points.