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dc.contributor.authorHurtado Díaz, Fernando Alfredo
dc.contributor.authorKorman, Matias
dc.contributor.authorVan Kreveld, Matias
dc.contributor.authorLöffler, Maarten
dc.contributor.authorSacristán Adinolfi, Vera
dc.contributor.authorShioura, Akiyoshi
dc.contributor.authorSilveira, Rodrigo Ignacio
dc.contributor.authorSpeckmann, Bettina
dc.contributor.authorTokuyama, Takeshi
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.identifier.citationHurtado, F., Korman, M., Van Kreveld, M., Löffler, M., Sacristán, V., Shioura, A., Silveira, R.I., Speckmann, B., Tokuyama, T. Colored spanning graphs for set visualization. "Computational geometry: theory and applications", Març 2018, vol. 68, p. 262-276.
dc.description.abstractWe 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 can be solved in polynomial time using matroid techniques. In addition, we discuss more efficient algorithms for the case in which points are located on a line or a circle, and also describe a fast (12¿+1)-approximation algorithm, where ¿ is the Steiner ratio.
dc.format.extent15 p.
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria computacional
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica
dc.subject.lcshNumerical analysis
dc.subject.lcshAlgebra, Homological
dc.subject.otherColored point set
dc.subject.otherMatroid intersection
dc.subject.otherMinimum spanning tree
dc.subject.otherSet visualization
dc.titleColored spanning graphs for set visualization
dc.subject.lemacAnàlisi numèrica
dc.subject.lemacÀlgebra homològica
dc.contributor.groupUniversitat Politècnica de Catalunya. DCG - Discrete and Combinatorial Geometry
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::65 Numerical analysis::65D Numerical approximation and computational geometry
dc.subject.amsClassificació AMS::55 Algebraic topology::55U Applied homological algebra and category theory
dc.rights.accessOpen Access
dc.description.versionPostprint (author's final draft)
upcommons.citation.authorHurtado, F., Korman, M., Van Kreveld, M., Löffler, M., Sacristán, V., Shioura, A., Silveira, R.I., Speckmann, B., Tokuyama, T.
upcommons.citation.publicationNameComputational geometry: theory and applications

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