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dc.contributor.authorFabila Monroy, Ruy
dc.contributor.authorGarcia Olaverri, Alfredo Martin
dc.contributor.authorHurtado Díaz, Fernando Alfredo
dc.contributor.authorJaume, Rafel
dc.contributor.authorPérez Lantero, Pablo
dc.contributor.authorSaumell, Maria
dc.contributor.authorSilveira, Rodrigo Ignacio
dc.contributor.authorTejel Altarriba, Francisco Javier
dc.contributor.authorUrrutia Galicia, Jorge
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.identifier.citationFabila, R., Garcia, A., Hurtado, F., Jaume, R., Pérez, P., Saumell, M., Silveira, R.I., Tejel, F., URRUTIA, J. Colored ray configurations. "Computational geometry: theory and applications", Maig 2018, vol. 68, p. 292-308.
dc.description.abstractWe study the cyclic color sequences induced at infinity by colored rays with apices being a given balanced finite bichromatic point set. We first study the case in which the rays are required to be pairwise disjoint. We derive a lower bound on the number of color sequences that can be realized from any such fixed point set and examine color sequences that can be realized regardless of the point set, exhibiting negative examples as well. We also provide a tight upper bound on the number of configurations that can be realized from a point set, and point sets for which there are asymptotically less configurations than that number. In addition, we provide algorithms to decide whether a color sequence is realizable from a given point set in a line or in general position. We address afterwards the variant of the problem where the rays are allowed to intersect. We prove that for some configurations and point sets, the number of ray crossings must be T(n2) and study then configurations that can be realized by rays that pairwise cross. We show that there are point sets for which the number of configurations that can be realized by pairwise-crossing rays is asymptotically smaller than the number of configurations realizable by pairwise-disjoint rays. We provide also point sets from which any configuration can be realized by pairwise-crossing rays and show that there is no configuration that can be realized by pairwise-crossing rays from every point set.
dc.format.extent17 p.
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject.lcshNumerical analysis
dc.subject.lcshComputing Methodologies
dc.subject.otherRay configurations
dc.subject.otherRed and blue points in the plane
dc.subject.otherColored rays
dc.subject.otherCircular sequences
dc.subject.otherEnumerative problems
dc.titleColored ray configurations
dc.subject.lemacAnàlisi numèrica
dc.contributor.groupUniversitat Politècnica de Catalunya. CGA -Computational Geometry and Applications
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::65 Numerical analysis::65D Numerical approximation and computational geometry
dc.subject.amsClassificació AMS::68 Computer science::68U Computing methodologies and applications
dc.rights.accessOpen Access
dc.description.versionPostprint (author's final draft)
upcommons.citation.authorFabila, R.; Garcia, A.; Hurtado, F.; Jaume, R.; Pérez, P.; Saumell, M.; Silveira, R.I.; Tejel, F.; URRUTIA, J.
upcommons.citation.publicationNameComputational geometry: theory and applications

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