Continuous surveillance of points by rotating floodlights
Let P and F be sets of n ≥ 2 and m ≥ 2 points in a plane, respectively. We study the problem of finding the minimum angle α ϵ [2Π/m, 2Π] such that one can install at each point of F a stationary rotating floodlight with illumination angle α, initially oriented in a suitable direction, in such a way...
| Autores: | , , , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2014 |
| 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:10256/21509 |
| Acceso en línea: | http://hdl.handle.net/10256/21509 |
| Access Level: | acceso abierto |
| Palabra clave: | Geometria computacional Computational geometry |
| Sumario: | Let P and F be sets of n ≥ 2 and m ≥ 2 points in a plane, respectively. We study the problem of finding the minimum angle α ϵ [2Π/m, 2Π] such that one can install at each point of F a stationary rotating floodlight with illumination angle α, initially oriented in a suitable direction, in such a way that, at all times, every target point of P is illuminated by at least one floodlight. All floodlights rotate clockwise at unit speed. We provide bounds for the case in which the elements of P ⋃ F are on a given line, and present exact results for the case in the plane in which we have two floodlights and many target points. We further consider the non-rotating version of the problem and look for the minimum angle α such that one can install a non-rotating floodlight with illumination angle α at each point of F, in such a way that every target point of P is illuminated by at least one floodlight. We show that this problem is NP-hard and hard to approximate |
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