An “Art Gallery Theorem” for pyramids
Every orthogonal polygon can be illuminated by ⌊ n / 4 ⌋ lights situated in the vertices of the polygon. In this paper we improve this bound for pyramids, showing that ⌈ n / 6 ⌉ guards situated in vertices are always sufficient and sometimes necessary for watching any pyramid of n vertices. Our proo...
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| Veröffentlicht in: | Information processing letters 2009-06, Vol.109 (13), p.719-721 |
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| container_title | Information processing letters |
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| creator | Abellanas, M. Canales, S. Hernández-Peñalver, G. |
| description | Every orthogonal polygon can be illuminated by
⌊
n
/
4
⌋
lights situated in the vertices of the polygon. In this paper we improve this bound for pyramids, showing that
⌈
n
/
6
⌉
guards situated in vertices are always sufficient and sometimes necessary for watching any pyramid of
n vertices. Our proof leads to a linear time algorithm for placing those guards. |
| doi_str_mv | 10.1016/j.ipl.2009.03.014 |
| format | Article |
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⌊
n
/
4
⌋
lights situated in the vertices of the polygon. In this paper we improve this bound for pyramids, showing that
⌈
n
/
6
⌉
guards situated in vertices are always sufficient and sometimes necessary for watching any pyramid of
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⌊
n
/
4
⌋
lights situated in the vertices of the polygon. In this paper we improve this bound for pyramids, showing that
⌈
n
/
6
⌉
guards situated in vertices are always sufficient and sometimes necessary for watching any pyramid of
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⌊
n
/
4
⌋
lights situated in the vertices of the polygon. In this paper we improve this bound for pyramids, showing that
⌈
n
/
6
⌉
guards situated in vertices are always sufficient and sometimes necessary for watching any pyramid of
n vertices. Our proof leads to a linear time algorithm for placing those guards.</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/j.ipl.2009.03.014</doi><tpages>3</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0020-0190 |
| ispartof | Information processing letters, 2009-06, Vol.109 (13), p.719-721 |
| issn | 0020-0190 1872-6119 |
| language | eng |
| recordid | cdi_proquest_journals_237292614 |
| source | Access via ScienceDirect (Elsevier) |
| subjects | Algorithmics. Computability. Computer arithmetics Algorithms Applied sciences Art galleries & museums Art Gallery Computational geometry Computer science control theory systems Exact sciences and technology Geometry Mathematics Miscellaneous Numerical analysis Numerical analysis. Scientific computation Numerical approximation Orthogonal polygon Polygons Pyramid Sciences and techniques of general use Studies Theoretical computing Visibility |
| title | An “Art Gallery Theorem” for pyramids |
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