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Connecting Red Cells in a Bicolour Voronoi Diagram

  • Manuel Abellanas
  • Antonio L. Bajuelos
  • Santiago Canales
  • Mercè Claverol
  • Gregorio Hernández
  • Inês Matos
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7579)

Abstract

Let S be a set of n + m sites, of which n are red and have weight w R , and m are blue and weigh w B . The objective of this paper is to calculate the minimum value of the red sites’ weight such that the union of the red Voronoi cells in the weighted Voronoi diagram of S is a connected region. This problem is solved for the multiplicatively-weighted Voronoi diagram in \(\mathcal{O}((n+m)^2 \log (nm))\) time and for both the additively-weighted and power Voronoi diagram in \(\mathcal{O}(nm \log (nm))\) time.

Keywords

Weighted Voronoi diagrams Bicolour Points 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Manuel Abellanas
    • 1
  • Antonio L. Bajuelos
    • 2
  • Santiago Canales
    • 3
  • Mercè Claverol
    • 4
  • Gregorio Hernández
    • 1
  • Inês Matos
    • 2
    • 4
  1. 1.Dept. de Matemática AplicadaUniversidad Politécnica de MadridSpain
  2. 2.Dept. de Matemática & CIDMAUniversidade de AveiroPortugal
  3. 3.Esc. Téc. Superior de IngenieríaUniversidad Pontificia Comillas de MadridSpain
  4. 4.Dept. de Matemàtica Aplicada II & IVUniversitat Politècnica de CatalunyaSpain

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