Convex blocking and partial orders on the plane
Let C = {c(1),..., c(n)} be a collection of disjoint closed bounded convex sets in the plane. Suppose that one of them, say c(1), represents a valuable object we want to uncover, and we are allowed to pick a direction alpha is an element of [0, 2 pi) along which we can translate (remove) the element...
| Autores: | , , , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2016 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:10256/11974 |
| Acceso en línea: | http://hdl.handle.net/10256/11974 |
| Access Level: | acceso embargado |
| Palabra clave: | Algorismes Algorithms Conjunts convexos Convex sets |
| Sumario: | Let C = {c(1),..., c(n)} be a collection of disjoint closed bounded convex sets in the plane. Suppose that one of them, say c(1), represents a valuable object we want to uncover, and we are allowed to pick a direction alpha is an element of [0, 2 pi) along which we can translate (remove) the elements of C, one at a time, while avoiding collisions. We study the problem of finding a direction alpha(0) such that the number of elements that have to be removed along alpha(0) before we can remove c(1) is minimized. We prove that if we have the sorted set D of directions defined by the tangents between pairs of elements of C, we can find alpha(0) in O(n(2)) time. We also discuss the problem of sorting D, in o(n(2)logn) time |
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