Colored ray configurations

Fabila-Monroy, R. ; García, A. (Universidad de Zaragoza) ; Hurtado, F. ; Jaume, R. ; Pérez-Lantero, P. ; Saumell, M. ; Silveira, R.I. ; Tejel, J. (Universidad de Zaragoza) ; Urrutia, J.

Resumen: 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.

Idioma: Inglés

DOI: 10.1016/j.comgeo.2017.05.008

Año: 2018

Publicado en: COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS 68 (2018), 292-308
ISSN: 0925-7721

Factor impacto JCR: 0.343 (2018)

Categ. JCR: MATHEMATICS, APPLIED rank: 248 / 254 = 0.976 (2018) - Q4 - T3
Categ. JCR: MATHEMATICS rank: 293 / 313 = 0.936 (2018) - Q4 - T3

Factor impacto SCIMAGO: 0.492 - Computational Mathematics (Q2) - Computational Theory and Mathematics (Q2) - Geometry and Topology (Q2) - Control and Optimization (Q2) - Computer Science Applications (Q2)

Financiación: info:eu-repo/grantAgreement/ES/DGA/E58
Financiación: info:eu-repo/grantAgreement/EC/H2020/734922/EU/Combinatorics of Networks and Computation/CONNECT
Financiación: info:eu-repo/grantAgreement/ES/MICINN/EUI-EURC-2011-4306
Financiación: info:eu-repo/grantAgreement/ES/MINECO/MTM2012-30951
Financiación: info:eu-repo/grantAgreement/ES/MINECO/MTM2015-63791-R
Financiación: info:eu-repo/grantAgreement/ES/MINECO/RYC-2013-14131

Tipo y forma: Article (PostPrint)

Área (Departamento): Área Estadís. Investig. Opera. (Dpto. Métodos Estadísticos)