On the Hyperbox – Hyperplane Intersection Problem
Finding the intersection between a hyperbox and a hyperplane can be computationally expensive specially for high dimensional problems. Naive algorithms have an exponential complexity. A border node is a node (in the graph induced by the hyperbox) at or next to the intersection of the hyperbox and th...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2009 |
| País: | Brasil |
| Institución: | Universidade Federal de Lavras (UFLA) |
| Repositorio: | INFOCOMP: Jornal de Ciência da Computação |
| Idioma: | inglés |
| OAI Identifier: | oai:infocomp.dcc.ufla.br:article/278 |
| Acceso en línea: | https://infocomp.dcc.ufla.br/index.php/infocomp/article/view/278 |
| Access Level: | acceso abierto |
| Palabra clave: | hyperbox hyperrectangle hyperplane vector graph searching |
| Sumario: | Finding the intersection between a hyperbox and a hyperplane can be computationally expensive specially for high dimensional problems. Naive algorithms have an exponential complexity. A border node is a node (in the graph induced by the hyperbox) at or next to the intersection of the hyperbox and the hyperplane. The algorithm proposed in this paper implements a systematic way to efficiently generate border nodes; given a border node, a subset of its incident edges is explored to determine one or more intersections. This systematic exploration allows us to focus on the border region, discarding the two regions before and after the plane. Pruning those regions produces a computational cost linear on the number of vertices of the hyperpolygon that represents the intersection. |
|---|