Cover Contact Graphs

  • Nieves Atienza
  • Natalia de Castro
  • Carmen Cortés
  • M. Ángeles Garrido
  • Clara I. Grima
  • Gregorio Hernández
  • Alberto Márquez
  • Auxiliadora Moreno
  • Martin Nöllenburg
  • José Ramon Portillo
  • Pedro Reyes
  • Jesús Valenzuela
  • Maria Trinidad Villar
  • Alexander Wolff
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4875)

Abstract

We study problems that arise in the context of covering certain geometric objects (so-called seeds, e.g., points or disks) by a set of other geometric objects (a so-called cover, e.g., a set of disks or homothetic triangles). We insist that the interiors of the seeds and the cover elements are pairwise disjoint, but they can touch. We call the contact graph of a cover a cover contact graph (CCG). We are interested in two types of tasks: (a) deciding whether a given seed set has a connected CCG, and (b) deciding whether a given graph has a realization as a CCG on a given seed set. Concerning task (a) we give efficient algorithms for the case that seeds are points and covers are disks or triangles. We show that the problem becomes NP-hard if seeds and covers are disks. Concerning task (b) we show that it is even NP-hard for point seeds and disk covers (given a fixed correspondence between vertices and seeds).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Nieves Atienza
    • 2
  • Natalia de Castro
    • 2
  • Carmen Cortés
    • 2
  • M. Ángeles Garrido
    • 2
  • Clara I. Grima
    • 2
  • Gregorio Hernández
    • 1
  • Alberto Márquez
    • 2
  • Auxiliadora Moreno
    • 2
  • Martin Nöllenburg
    • 3
  • José Ramon Portillo
    • 2
  • Pedro Reyes
    • 2
  • Jesús Valenzuela
    • 2
  • Maria Trinidad Villar
    • 2
  • Alexander Wolff
    • 4
  1. 1.Dept. Matemática Aplicada, Fac. InformáticaUniv. Politécnica de MadridSpain
  2. 2.Universidad de SevillaSpain
  3. 3.Fakultät für InformatikUniversität KarlsruheGermany
  4. 4.Faculteit Wiskunde en InformaticaTU EindhovenThe Netherlands

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