Cooperative half-guards in art galleries
In any simple polygonal art gallery with n walls, we show that it is possible to place floor(n/2)-1 guards whose range of vision is 180 degrees in such a way that every interior point of the gallery can be seen by one of them, and such that the mutual visibility graph formed by the guards is connect...
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| creator | Florentino, Daniel Moy, Ethan Muth, Robert |
| description | In any simple polygonal art gallery with n walls, we show that it is possible
to place floor(n/2)-1 guards whose range of vision is 180 degrees in such a way
that every interior point of the gallery can be seen by one of them, and such
that the mutual visibility graph formed by the guards is connected. This upper
bound is tight, in that there exist galleries which require this number of
guards, and equals the known result for guards with full 360 degree range of
vision. We also show that for orthogonal art galleries, this result may be
improved to floor(n/2)-2 guards with 180 degree range of vision. |
| doi_str_mv | 10.48550/arxiv.2007.03737 |
| format | Article |
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to place floor(n/2)-1 guards whose range of vision is 180 degrees in such a way
that every interior point of the gallery can be seen by one of them, and such
that the mutual visibility graph formed by the guards is connected. This upper
bound is tight, in that there exist galleries which require this number of
guards, and equals the known result for guards with full 360 degree range of
vision. We also show that for orthogonal art galleries, this result may be
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to place floor(n/2)-1 guards whose range of vision is 180 degrees in such a way
that every interior point of the gallery can be seen by one of them, and such
that the mutual visibility graph formed by the guards is connected. This upper
bound is tight, in that there exist galleries which require this number of
guards, and equals the known result for guards with full 360 degree range of
vision. We also show that for orthogonal art galleries, this result may be
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to place floor(n/2)-1 guards whose range of vision is 180 degrees in such a way
that every interior point of the gallery can be seen by one of them, and such
that the mutual visibility graph formed by the guards is connected. This upper
bound is tight, in that there exist galleries which require this number of
guards, and equals the known result for guards with full 360 degree range of
vision. We also show that for orthogonal art galleries, this result may be
improved to floor(n/2)-2 guards with 180 degree range of vision.</abstract><doi>10.48550/arxiv.2007.03737</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Combinatorics |
| title | Cooperative half-guards in art galleries |
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