Art Gallery Problem with Rook and Queen Vision

被引：1

作者：

Alpert, Hannah ^{[1
]}

Roldan, Erika ^{[2
]}

机构：

[1] Univ British Columbia, 1984 Math Rd, Vancouver, BC, Canada

[2] Tech Univ Munich, Zentrum Math, Munich, Germany

来源：

GRAPHS AND COMBINATORICS | 2021年 / 37卷 / 02期

关键词：

Art gallery theorem; NP-hardness; polyomino; Computational geometry; Chessboard complex; Visibility coverage; Guard number; Domination problem; N-Queens Problem; COMPUTATIONAL-COMPLEXITY; THEOREM;

D O I：

10.1007/s00373-020-02272-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

How many chess rooks or queens does it take to guard all 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 bn 2c rooks or bn 3c queens are sufficient and sometimes necessary to guard a polyomino with n tiles. We then prove that finding the minimum number of rooks or queens needed to guard a polyomino is NP-hard. These results also apply to d-dimensional rooks and queens on d-dimensional polycubes. Finally, we use bipartite matching theorems to describe sets of non-attacking rooks on polyominoes.

引用

页码：621 / 642

页数：22

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