A chord is a straight line within a polygon connecting two non-adjacent vertices. Given such
a chord c of a polygon, we denote by n (c) the number of vertices visible from c. The chord …

Given a simple polygon P on n vertices, two points x, y in P are said to be visible to each
other if the line segment between x and y is contained in P. The Point Guard Art Gallery …

Given a simple polygon $\mathcal {P} $ on $ n $ vertices, two points $ x, y $ in $\mathcal {P}
$ are said to be visible to each other if the line segment between $ x $ and $ y $ is contained …

Abstract A graph G=(V, E) is terrain-like if one can assign a unique integer from the range
[1..| V|] to each vertex in V, such that, if both {i, k} and {j, l} are in E, for any i< j< k< l, then so is …

The ArtGallery problem is a fundamental visibility problem in Computational Geometry. The
input consists of a simple polygon P,(possibly infinite) sets G and C of points within P, and …

In the Art Gallery Problem we are given a polygon $ P\subset [0, L]^ 2$ on $ n $ vertices and
a number $ k $. We want to find a guard set $ G $ of size $ k $, such that each point in $ P …

The problem of vertex guarding a simple polygon was first studied by Subir K. Ghosh (1987),
who presented a polynomial-time O (\log n) O (log n)-approximation algorithm for placing as …

A terrain is an x-monotone polygonal curve, ie, successive vertices have increasing x-
coordinates. Terrain Guarding can be seen as a special case of the famous art gallery …

The purpose of this invited talk is threefold: provide a brief introduction to both
Parameterized Analysis and algorithmic research of visibility problems, and to address a few …

Given a simple polygon $\cal P $, in the Art Gallery problem the goal is to find the minimum
number of guards needed to cover the entire $\cal P $, where a guard is a point and can see …