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...

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Detalles Bibliográficos
Autores: Lara, Carlos, Flores, Juan J., Calderon, Felix
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
Descripción
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.