Colored spanning graphs for set visualization

Ferran Hurtado, Cozzetti Matias Korman, Marc Van Kreveld, Maarten Löffler, Vera Sacristán, Rodrigo I. Silveira, Bettina Speckmann

Research output: Chapter in Book/Report/Conference proceedingConference contribution

10 Citations (Scopus)

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 (1/2ρ+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.

Original languageEnglish
Title of host publicationGraph Drawing - 21st International Symposium, GD 2013, Revised Selected Papers
Pages280-291
Number of pages12
DOIs
Publication statusPublished - 2013 Dec 1
Externally publishedYes
Event21st International Symposium on Graph Drawing, GD 2013 - Bordeaux, France
Duration: 2013 Sep 232013 Sep 25

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8242 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other21st International Symposium on Graph Drawing, GD 2013
CountryFrance
CityBordeaux
Period13/9/2313/9/25

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Hurtado, F., Korman, C. M., Van Kreveld, M., Löffler, M., Sacristán, V., Silveira, R. I., & Speckmann, B. (2013). Colored spanning graphs for set visualization. In Graph Drawing - 21st International Symposium, GD 2013, Revised Selected Papers (pp. 280-291). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8242 LNCS). https://doi.org/10.1007/978-3-319-03841-4-25