The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Masalah galeri seni adalah untuk mencari satu set pengawal yang bersama-sama boleh memerhati setiap titik bahagian dalam poligon P. Kami mengkaji varian kromatik masalah, di mana setiap pengawal diberikan salah satu daripadanya k warna yang berbeza. The masalah galeri seni kromatik adalah untuk mencari pengawal yang ditetapkan untuk P supaya tiada dua pengawal dengan warna yang sama mempunyai kawasan keterlihatan bertindih. Kami mengkaji versi keputusan masalah ini untuk poligon ortogon dengan r-keterlihatan apabila bilangan warna adalah k=2. Di sini, dua mata adalah r-kelihatan jika segi empat tepat sejajar paksi terkecil yang mengandunginya terletak sepenuhnya dalam poligon. Dalam kertas kerja ini, ditunjukkan bahawa menentukan sama ada terdapat r-pengadang kebolehlihatan ditetapkan untuk poligon ortogon dengan lubang supaya tiada dua pengadang dengan warna yang sama mempunyai kawasan keterlihatan bertindih adalah NP-keras apabila bilangan warna adalah k= 2.
Chuzo IWAMOTO
Hiroshima University
Tatsuaki IBUSUKI
Hiroshima University
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Salinan
Chuzo IWAMOTO, Tatsuaki IBUSUKI, "Chromatic Art Gallery Problem with r-Visibility is NP-Complete" in IEICE TRANSACTIONS on Fundamentals,
vol. E104-A, no. 9, pp. 1108-1115, September 2021, doi: 10.1587/transfun.2020DMP0006.
Abstract: The art gallery problem is to find a set of guards who together can observe every point of the interior of a polygon P. We study a chromatic variant of the problem, where each guard is assigned one of k distinct colors. The chromatic art gallery problem is to find a guard set for P such that no two guards with the same color have overlapping visibility regions. We study the decision version of this problem for orthogonal polygons with r-visibility when the number of colors is k=2. Here, two points are r-visible if the smallest axis-aligned rectangle containing them lies entirely within the polygon. In this paper, it is shown that determining whether there is an r-visibility guard set for an orthogonal polygon with holes such that no two guards with the same color have overlapping visibility regions is NP-hard when the number of colors is k=2.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2020DMP0006/_p
Salinan
@ARTICLE{e104-a_9_1108,
author={Chuzo IWAMOTO, Tatsuaki IBUSUKI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Chromatic Art Gallery Problem with r-Visibility is NP-Complete},
year={2021},
volume={E104-A},
number={9},
pages={1108-1115},
abstract={The art gallery problem is to find a set of guards who together can observe every point of the interior of a polygon P. We study a chromatic variant of the problem, where each guard is assigned one of k distinct colors. The chromatic art gallery problem is to find a guard set for P such that no two guards with the same color have overlapping visibility regions. We study the decision version of this problem for orthogonal polygons with r-visibility when the number of colors is k=2. Here, two points are r-visible if the smallest axis-aligned rectangle containing them lies entirely within the polygon. In this paper, it is shown that determining whether there is an r-visibility guard set for an orthogonal polygon with holes such that no two guards with the same color have overlapping visibility regions is NP-hard when the number of colors is k=2.},
keywords={},
doi={10.1587/transfun.2020DMP0006},
ISSN={1745-1337},
month={September},}
Salinan
TY - JOUR
TI - Chromatic Art Gallery Problem with r-Visibility is NP-Complete
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1108
EP - 1115
AU - Chuzo IWAMOTO
AU - Tatsuaki IBUSUKI
PY - 2021
DO - 10.1587/transfun.2020DMP0006
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E104-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2021
AB - The art gallery problem is to find a set of guards who together can observe every point of the interior of a polygon P. We study a chromatic variant of the problem, where each guard is assigned one of k distinct colors. The chromatic art gallery problem is to find a guard set for P such that no two guards with the same color have overlapping visibility regions. We study the decision version of this problem for orthogonal polygons with r-visibility when the number of colors is k=2. Here, two points are r-visible if the smallest axis-aligned rectangle containing them lies entirely within the polygon. In this paper, it is shown that determining whether there is an r-visibility guard set for an orthogonal polygon with holes such that no two guards with the same color have overlapping visibility regions is NP-hard when the number of colors is k=2.
ER -