Colored Spanning Graphs for Set Visualization

  • Ferran Hurtado
  • Matias Korman
  • Marc van Kreveld
  • Maarten Löffler
  • Vera Sacristán
  • Rodrigo I. Silveira
  • Bettina Speckmann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8242)

Abstract

We study an algorithmic problem that is motivated by ink minimization for sparse set visualizations. Our input is a set of points in the plane which are either blue, red, or purple. Blue points belong exclusively to the blue set, red points belong exclusively to the red set, and purple points belong to both sets. A red-blue-purple spanning graph (RBP spanning graph) is a set of edges connecting the points such that the subgraph induced by the red and purple points is connected, and the subgraph induced by the blue and purple points is connected.

We study the geometric properties of minimum RBP spanning graphs and the algorithmic problems associated with computing them. Specifically, we show that the general problem is NP-hard. Hence we give an \((\frac 12\rho+1)\)-approximation, where ρ is the Steiner ratio. We also present efficient exact solutions if the points are located on a line or a circle. Finally we consider extensions to more than two sets.

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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Ferran Hurtado
    • 1
  • Matias Korman
    • 1
  • Marc van Kreveld
    • 2
  • Maarten Löffler
    • 2
  • Vera Sacristán
    • 1
  • Rodrigo I. Silveira
    • 4
    • 1
  • Bettina Speckmann
    • 3
  1. 1.Dept. de Matemàtica Aplicada IIUniversitat Politècnica de CatalunyaSpain
  2. 2.Dept. of Computing and Information SciencesUtrecht UniversityThe Netherlands
  3. 3.Dept. of Mathematics and Computer ScienceTechnical University EindhovenThe Netherlands
  4. 4.Dept. de MatemáticaUniversidade de AveiroPortugal

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