Related papers: The Parameterized Hardness of Art Gallery Problems
In this paper, we study the Contiguous Art Gallery Problem, introduced by Thomas C. Shermer at the 2024 Canadian Conference on Computational Geometry, a variant of the classical art gallery problem from 1973 by Victor Klee. In the…
We study the problem of guarding the boundary of a simple polygon with a minimum number of guards such that each guard covers a contiguous portion of the boundary. First, we present a simple greedy algorithm for this problem that returns a…
We explore the problem of $M$-guarding polygons with holes using $k$-visibility guards, where a set of guards is said to $M$-guard a polygon if every point in the polygon is visible to at least $M$ guards, with the constraint that there may…
We consider a generalization of the classical Art Gallery Problem, where instead of a light source, the guards, called $k$-transmitters, model a wireless device with a signal that can pass through at most $k$ walls. We show it is NP-hard to…
A hidden guard set $ G $ is a set of point guards in polygon $ P $ that all points of the polygon are visible from some guards in $ G $ under the constraint that no two guards may see each other. In this paper, we consider the problem for…
The purpose of the current study is to investigate a special case of art gallery problem, namely Sculpture Garden Problem. In the said problem, for a given polygon $P$, the ultimate goal is to place the minimum number of guards to define…
We study the problem of placing a set $T$ of broadcast towers in a simple polygon $P$ in order for any point to locate itself in the interior of $P$. Let $V(p)$ denote the visibility polygon of a point $p$, as the set of all points $q \in…
We study the Art Gallery Problem under $k$-hop visibility in polyominoes. In this visibility model, two unit squares of a polyomino can see each other if and only if the shortest path between the respective vertices in the dual graph of the…
We show the following problems are in $\textsf{P}$: 1. The contiguous art gallery problem -- a variation of the art gallery problem where each guard can protect a contiguous interval along the boundary of a simple polygon. This was posed at…
We study the Art Gallery Problem for face guards in polyhedral environments. The problem can be informally stated as: how many (not necessarily convex) windows should we place on the external walls of a dark building, in order to completely…
We study the problem of colouring the vertices of a polygon, such that every viewer in it can see a unique colour. The goal is to minimise the number of colours used. This is also known as the conflict-free chromatic guarding problem with…
Given a polygon $H$ in the plane, the art gallery problem calls for fining the smallest set of points in $H$ from which every other point in $H$ is seen. We give a deterministic algorithm that, given any polygon $H$ with $h$ holes, $n$…
A polygonal art gallery can be observed by guards placed at one third of its corners. However, the strategy of placing guards at every third corner does not work for all art galleries. In this note, we provide an example of a nine-sided art…
A sliding camera inside an orthogonal polygon $P$ is a point guard that travels back and forth along an orthogonal line segment $\gamma$ in $P$. The sliding camera $g$ can see a point $p$ in $P$ if the perpendicular from $p$ onto $\gamma$…
We will consider some extensions of the polygonal art gallery problem. In a recent paper Morrison has shown the smallest (9 sides) example of an art gallery that cannot be observed by guards placed in every third corner. Author also…
We study the problem of guarding orthogonal art galleries with horizontal mobile guards (alternatively, vertical) and point guards, using "rectangular vision". We prove a sharp bound on the minimum number of point guards required to cover…
This thesis focuses on two concepts which are widely studied in the field of computational geometry. Namely, visibility and unit disk graphs. In the field of visibility, we have studied the conflict-free chromatic guarding of polygons, for…
A point visibility graph is a graph induced by a set of points in the plane, where every vertex corresponds to a point, and two vertices are adjacent whenever the two corresponding points are visible from each other, that is, the open…
A terrain is an x-monotone polygonal curve, i.e., successive vertices have increasing x-coordinates. Terrain Guarding can be seen as a special case of the famous art gallery problem where one has to place at most $k$ guards on a terrain…
A point visibility graph is a graph induced by a set of points in the plane where the vertices of the graph represent the points in the point set and two vertices are adjacent if and only if no other point from the point set lies on the…