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Efficient computation of minimum-area rectilinear convex hull under rotation and generalizations
dc.contributor.author | Alegría Galicia, Carlos |
dc.contributor.author | Orden Martin, David |
dc.contributor.author | Seara Ojea, Carlos |
dc.contributor.author | Urrutia Galicia, Jorge |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2021-03-03T10:34:05Z |
dc.date.available | 2022-03-01T01:26:07Z |
dc.date.issued | 2021-03 |
dc.identifier.citation | Alegría-Galicia, C. [et al.]. Efficient computation of minimum-area rectilinear convex hull under rotation and generalizations. "Journal of Global Optimization", Març 2021, vol. 79, núm. 3, p. 687-714. |
dc.identifier.issn | 1573-2916 |
dc.identifier.other | https://arxiv.org/pdf/1710.10888.pdf |
dc.identifier.uri | http://hdl.handle.net/2117/340814 |
dc.description | This is a post-peer-review, pre-copyedit version of an article published in Journal of Global Optimization. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10898-020-00953-5 |
dc.description.abstract | Let P be a set of n points in the plane. We compute the value of ¿¿[0,2p) for which the rectilinear convex hull of P, denoted by RHP(¿), has minimum (or maximum) area in optimal O(nlogn) time and O(n) space, improving the previous O(n2) bound. Let O be a set of k lines through the origin sorted by slope and let ai be the sizes of the 2k angles defined by pairs of two consecutive lines, i=1,…,2k. Let Ti=p-ai and T=min{Ti:i=1,…,2k}. We obtain: (1) Given a set O such that T=p2, we provide an algorithm to compute the O-convex hull of P in optimal O(nlogn) time and O(n) space; If T<p2, the time and space complexities are O(nTlogn) and O(nT) respectively. (2) Given a set O such that T=p2, we compute and maintain the boundary of the O¿-convex hull of P for ¿¿[0,2p) in O(knlogn) time and O(kn) space, or if T<p2, in O(knTlogn) time and O(knT) space. (3) Finally, given a set O such that T=p2, we compute, in O(knlogn) time and O(kn) space, the angle ¿¿[0,2p) such that the O¿-convex hull of P has minimum (or maximum) area over all ¿¿[0,2p). |
dc.description.sponsorship | Carlos Alegría: Research supported in part by UNAM Project PAEP, and by MIUR Proj. “AHeAD” No. 20174LF3T8. David Orden: Research supported by Projects MTM2017-83750-P of the Spanish Ministry of Science (AEI/FEDER, UE), and Project PID2019-104129GB-I00 of the Spanish Ministry of Science and Innovation. Carlos Seara: Research supported by Projects Gen. Cat. DGR 2017SGR1640, MINECO MTM2015-63791-R, and Project PID2019-104129GB-I00 of the Spanish Ministry of Science and Innovation. Jorge Urrutia: Research supported in part by SEP-CONACYT 80268, PAPPIIT IN102117 Programa de Apoyo a la Investigación e Innovación Tecnológica UNAM. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 734922. |
dc.format.extent | 28 p. |
dc.language.iso | eng |
dc.publisher | Springer Nature |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Optimització |
dc.subject.lcsh | Operations research |
dc.subject.other | Rectilinear convex hull |
dc.subject.other | Restricted orientation convex hull |
dc.subject.other | Minimum area |
dc.title | Efficient computation of minimum-area rectilinear convex hull under rotation and generalizations |
dc.type | Article |
dc.subject.lemac | Optimització matemàtica |
dc.contributor.group | Universitat Politècnica de Catalunya. CGA - Computational Geometry and Applications |
dc.identifier.doi | 10.1007/s10898-020-00953-5 |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::90 Operations research, mathematical programming::90B Operations research and management science |
dc.relation.publisherversion | https://link.springer.com/article/10.1007/s10898-020-00953-5 |
dc.rights.access | Open Access |
local.identifier.drac | 30371529 |
dc.description.version | Postprint (author's final draft) |
dc.relation.projectid | info:eu-repo/grantAgreement/EC/H2020/734922/EU/Combinatorics of Networks and Computation/CONNECT |
dc.relation.projectid | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-104129GB-I00/ES/TEORIA Y APLICACIONES DE CONFIGURACIONES DE PUNTOS Y REDES/ |
local.citation.author | Alegría-Galicia , C.; Orden, D.; Seara, C.; URRUTIA, J. |
local.citation.publicationName | Journal of Global Optimization |
local.citation.volume | 79 |
local.citation.number | 3 |
local.citation.startingPage | 687 |
local.citation.endingPage | 714 |
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