Colored spanning graphs for set visualization

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

doi:10.1007/978-3-319-03841-4_25

Colored spanning graphs for set visualization

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

INF - System Information Sciences

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English
Title of host publication	Graph Drawing - 21st International Symposium, GD 2013, Revised Selected Papers
Publisher	Springer Verlag
Pages	280-291
Number of pages	12
ISBN (Print)	9783319038407
DOIs	https://doi.org/10.1007/978-3-319-03841-4_25
Publication status	Published - 2013
Event	21st International Symposium on Graph Drawing, GD 2013 - Bordeaux, France Duration: 2013 Sep 23 → 2013 Sep 25

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	8242 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	21st International Symposium on Graph Drawing, GD 2013
Country	France
City	Bordeaux
Period	13/9/23 → 13/9/25

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

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Hurtado, F., Korman, 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). Springer Verlag. https://doi.org/10.1007/978-3-319-03841-4_25

Colored spanning graphs for set visualization. / Hurtado, Ferran; Korman, Matias; Van Kreveld, Marc; Löffler, Maarten; Sacristán, Vera; Silveira, Rodrigo I.; Speckmann, Bettina.

Graph Drawing - 21st International Symposium, GD 2013, Revised Selected Papers. Springer Verlag, 2013. p. 280-291 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8242 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Hurtado, F, Korman, M, Van Kreveld, M, Löffler, M, Sacristán, V, Silveira, RI & Speckmann, B 2013, Colored spanning graphs for set visualization. in Graph Drawing - 21st International Symposium, GD 2013, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8242 LNCS, Springer Verlag, pp. 280-291, 21st International Symposium on Graph Drawing, GD 2013, Bordeaux, France, 13/9/23. https://doi.org/10.1007/978-3-319-03841-4_25

Hurtado F, Korman M, Van Kreveld M, Löffler M, Sacristán V, Silveira RI et al. Colored spanning graphs for set visualization. In Graph Drawing - 21st International Symposium, GD 2013, Revised Selected Papers. Springer Verlag. 2013. p. 280-291. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-03841-4_25

Hurtado, Ferran ; Korman, Matias ; Van Kreveld, Marc ; Löffler, Maarten ; Sacristán, Vera ; Silveira, Rodrigo I. ; Speckmann, Bettina. / Colored spanning graphs for set visualization. Graph Drawing - 21st International Symposium, GD 2013, Revised Selected Papers. Springer Verlag, 2013. pp. 280-291 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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AU - Silveira, Rodrigo I.

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AB - 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.

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Colored spanning graphs for set visualization

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