Art gallery problem with rook and queen vision
Computational Complexity
2018-11-21 v2 Combinatorics
Abstract
How many chess rooks or queens does it take to guard all the squares of a given polyomino, the union of square tiles from a square grid? This question is a version of the art gallery problem in which the guards can "see" whichever squares the rook or queen attacks. We show that floor(n/2) rooks or floor(n/3) queens are sufficient and sometimes necessary to guard a polyomino with n tiles. We also prove that finding the minimum number of rooks or the minimum number of queens needed to guard a polyomino is NP-hard. These results also apply to d-dimensional rooks and queens on d-dimensional polycubes. We also use bipartite matching theorems to describe sets of non-attacking rooks on polyominoes.
Cite
@article{arxiv.1810.10961,
title = {Art gallery problem with rook and queen vision},
author = {Hannah Alpert and Érika Roldán},
journal= {arXiv preprint arXiv:1810.10961},
year = {2018}
}