Farthest color Voronoi diagrams: complexity and algorithms
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| Titel: | Farthest color Voronoi diagrams: complexity and algorithms |
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| Autoren: | Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. CGA - Computational Geometry and Applications, Mantas, Ioannis, Papadopoulou, Evanthia, Sacristán Adinolfi, Vera, Silveira, Rodrigo Ignacio |
| Verlagsinformationen: | Springer 2021 |
| Publikationsart: | Electronic Resource |
| Abstract: | The farthest-color Voronoi diagram (FCVD) is a farthestsite Voronoi structure defined on a family P of m point-clusters in the plane, where the total number of points is n. The FCVD finds applications in problems related to color spanning objects and facility location. We identify structural properties of the FCVD, refine its combinatorial complexity bounds, and list conditions under which the diagram has O(n) complexity. We show that the diagram may have complexity ¿(n + m2 ) even if clusters have disjoint convex hulls. We present construction algorithms with running times ranging from O(n log n), when certain conditions are met, to O((n+s(P)) log3 n) in general, where s(P) is a parameter reflecting the number of straddles between pairs of clusters in P (s(P) ¿ O(mn)). A pair of points q1, q2 ¿ Q is said to straddle p1, p2 ¿ P if the line segment q1q2 intersects (straddles) the line through p1, p2 and the disks through (p1, p2, q1) and (p1, p2, q2) contain no points of P, Q. The complexity of the diagram is shown to be O(n + s(P)). Peer Reviewed Postprint (author's final draft) |
| Index Begriffe: | Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica::Anàlisi multivariant, Multivariate analysis, Farthest color · MaxMin · Voronoi diagram · Point clusters, Anàlisi multivariable, Classificació AMS::62 Statistics::62H Multivariate analysis, Conference report |
| URL: | info:eu-repo/grantAgreement/EC/H2020/734922/EU/Combinatorics of Networks and Computation/CONNECT |
| Verfügbarkeit: | Open access content. Open access content Restricted access - publisher's policy |
| Anmerkung: | 13 p. application/pdf English |
| Other Numbers: | HGF oai:upcommons.upc.edu:2117/340947 Mantas, I. [et al.]. Farthest color Voronoi diagrams: complexity and algorithms. A: Latin American Theoretical Informatics Symposium. "LATIN 2020: Theoretical Informatics: 14th Latin American Symposium: São Paulo, Brazil: 5-8 january 5, 2021: proceedings". Berlín: Springer, 2021, p. 283-295. ISBN 978-3-030-61791-2. DOI 10.1007/978-3-030-61792-9_23. 978-3-030-61791-2 10.1007/978-3-030-61792-9_23 1247081582 |
| Originalquelle: | UNIV POLITECNICA DE CATALUNYA From OAIster®, provided by the OCLC Cooperative. |
| Dokumentencode: | edsoai.on1247081582 |
| Datenbank: | OAIster |
Nájsť tento článok vo Web of Science | Abstract: | The farthest-color Voronoi diagram (FCVD) is a farthestsite Voronoi structure defined on a family P of m point-clusters in the plane, where the total number of points is n. The FCVD finds applications in problems related to color spanning objects and facility location. We identify structural properties of the FCVD, refine its combinatorial complexity bounds, and list conditions under which the diagram has O(n) complexity. We show that the diagram may have complexity ¿(n + m2 ) even if clusters have disjoint convex hulls. We present construction algorithms with running times ranging from O(n log n), when certain conditions are met, to O((n+s(P)) log3 n) in general, where s(P) is a parameter reflecting the number of straddles between pairs of clusters in P (s(P) ¿ O(mn)). A pair of points q1, q2 ¿ Q is said to straddle p1, p2 ¿ P if the line segment q1q2 intersects (straddles) the line through p1, p2 and the disks through (p1, p2, q1) and (p1, p2, q2) contain no points of P, Q. The complexity of the diagram is shown to be O(n + s(P)).<br />Peer Reviewed<br />Postprint (author's final draft) |
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