Colored spanning graphs for set visualization

F. Hurtado, M. Korman, M.J. Kreveld, van, M. Löffler, V. Sacristán, R.I. Silveira, B. Speckmann

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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 (½ ¿ + 1)-approximation, where ¿ 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, Bordeaux, France, September 23-25, 2013, Revised Selected Papers
EditorsS. Wismath, A. Wolff
Place of PublicationBerlin
PublisherSpringer
Pages280-291
ISBN (Print)78-3-319-03840-7
DOIs
Publication statusPublished - 2013
Event21st International Symposium on Graph Drawing (GD 2013) - Bordeaux, France
Duration: 23 Sep 201325 Sep 2013
Conference number: 21
http://gd2013.labri.fr/

Publication series

NameLecture Notes in Computer Science
Volume8242
ISSN (Print)0302-9743

Conference

Conference21st International Symposium on Graph Drawing (GD 2013)
Abbreviated titleGD 2013
CountryFrance
CityBordeaux
Period23/09/1325/09/13
Other21st International Symposium on Graph Drawing
Internet address

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