Guarding polyominoes

Authors:
Therese Biedl;Mohammad T. Irfan;Justin Iwerks;Joondong Kim;Joseph S.B. Mitchell
Affiliations:
University of Waterloo, Waterloo, ON, Canada;Stony Brook University, Stony Brook, NY, USA;Stony Brook University, Stony Brook, NY, USA;Stony Brook University, Stony Brook, NY, USA;Stony Brook University, Stony Brook, NY, USA
Venue:
Proceedings of the twenty-seventh annual symposium on Computational geometry
Year:
2011

Citing 9
Cited 1

A short proof of the rectilinear art gallery theorem

SIAM Journal on Algebraic and Discrete Methods
Computational complexity of art gallery problems

IEEE Transactions on Information Theory
Art gallery theorems and algorithms

Art gallery theorems and algorithms
On the rectilinear art gallery problem

Proceedings of the seventeenth international colloquium on Automata, languages and programming
Guarding galleries and terrains

Information Processing Letters
On guarding the vertices of rectilinear domains

Computational Geometry: Theory and Applications
A Constant-Factor Approximation Algorithm for Optimal 1.5D Terrain Guarding

SIAM Journal on Computing
Note: Approximation algorithms for art gallery problems in polygons

Discrete Applied Mathematics
Approximate guarding of monotone and rectilinear polygons

ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming

Guarding thin orthogonal polygons is hard

FCT'13 Proceedings of the 19th international conference on Fundamentals of Computation Theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

We explore the art gallery problem for the special case that the domain (gallery) P is an m-polyomino, a polyform whose cells are m unit squares. We study the combinatorics of guarding polyominoes in terms of the parameter m, in contrast with the traditional parameter n, the number of vertices of P; in particular, we show that floor((m+1)/3) point guards are always sufficient and sometimes necessary to cover an m-polyomino. When m d 3n/4 - 4, the point guard sufficiency condition yields a strictly lower guard number than floor(n/4), given by the art gallery theorem for orthogonal polygons. When pixels behave themselves like guards (pixel guards), we prove that floor(3m/11) + 1 guards are sufficient and sometimes necessary to cover an m-polyomino. We also study the algorithmic complexity of computing optimal guard sets for polyominoes. We prove that determining the guard number of a given m-polyomino is NP-hard. We provide polynomial-time algorithms to solve exactly some special cases in which the polyomino is "thin".