78058 20191122145055.0 doi 10.1016/j.comgeo.2017.05.008 sideral 101841 ART-2018-101841 eng Fabila-Monroy, R. Colored ray configurations 2018 Access copy available to the general public Unrestricted We 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. info:eu-repo/grantAgreement/ES/MINECO/RYC-2013-14131 info:eu-repo/grantAgreement/ES/MINECO/MTM2015-63791-R info:eu-repo/grantAgreement/ES/MINECO/MTM2012-30951 info:eu-repo/grantAgreement/ES/MICINN/EUI-EURC-2011-4306 This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No H2020 734922-CONNECT info:eu-repo/grantAgreement/EC/H2020/734922/EU/Combinatorics of Networks and Computation/CONNECT info:eu-repo/grantAgreement/ES/DGA/E58 info:eu-repo/semantics/openAccess by-nc-nd http://creativecommons.org/licenses/by-nc-nd/3.0/es/ 0.343 2018 MATHEMATICS, APPLIED 248 / 254 = 0.976 2018 Q4 T3 MATHEMATICS 293 / 313 = 0.936 2018 Q4 T3 0.492 2018 Computational Mathematics 2018 Q2 Computational Theory and Mathematics 2018 Q2 Geometry and Topology 2018 Q2 Control and Optimization 2018 Q2 Computer Science Applications 2018 Q2 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion (orcid)0000-0002-6519-1472 García, A. Universidad de Zaragoza Hurtado, F. Jaume, R. Pérez-Lantero, P. Saumell, M. Silveira, R.I. (orcid)0000-0002-9543-7170 Tejel, J. Universidad de Zaragoza Urrutia, J. 2007 265 Universidad de Zaragoza Dpto. Métodos Estadísticos Área Estadís. Investig. Opera. 68 (2018), 292-308 Comput. geom. COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS 0925-7721 958769 http://zaguan.unizar.es/record/78058/files/texto_completo.pdf Postprint 74229 http://zaguan.unizar.es/record/78058/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:78058 articulos driver 2019-11-22-14:45:31 ARTICLE