Related papers: A Linear-Time Approximation Algorithm for the Orth…
Terrain Guarding Problem(TGP), which is known to be NP-complete, asks to find a smallest set of guard locations on a terrain $T$ such that every point on $T$ is visible by a guard. Here, we study this problem on 1.5D orthogonal terrains…
Herein, we consider the continuous 1.5-dimensional(1.5D) terrain guarding problem with two-sided guarding. We provide an x-monotone chain T and determine the minimal number of vertex guards such that all points of T have been two-sided…
A terrain T is an x-monotone polygonal chain in the plane; T is orthogonal if each edge of T is either horizontal or vertical. In this paper, we give an exact algorithm for the problem of guarding the convex vertices of an orthogonal…
In the continuous 1.5-dimensional terrain guarding problem we are given an $x$-monotone chain (the \emph{terrain} $T$) and ask for the minimum number of point guards (located anywhere on $T$), such that all points of $T$ are covered by at…
We present a 4-approximation algorithm for the problem of placing a fewest guards on a 1.5D terrain so that every point of the terrain is seen by at least one guard. This improves on the currently best approximation factor of 5. Our method…
Given an $x$-monotone polygonal chain $T$ with $n$ vertices, and an integer $k$, we consider the problem of finding the lowest horizontal line $L$ lying above $T$ with $k$ point guards lying on $L$, so that every point on the chain is…
In the NP-hard continuous 1.5D Terrain Guarding Problem (TGP) we are given an $x$-monotone chain of line segments in $\mathbb{R}^2$ (the terrain $T$) and ask for the minimum number of guards (located anywhere on $T$) required to guard all…
We present an optimal, linear-time algorithm for the following version of terrain guarding: given a 1.5D terrain and a horizontal line, place the minimum number of guards on the line to see all of the terrain. We prove that the cardinality…
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…
A set $G$ of points on a 1.5-dimensional terrain, also known as an $x$-monotone polygonal chain, is said to guard the terrain if any point on the terrain is 'seen' by a point in $G$. Two points on the terrain see each other if and only if…
There exist many variants of guarding an orthogonal polygon in an orthogonal fashion: sometimes a guard can see an entire rectangle, or along a staircase, or along an orthogonal path with at most $k$ bends. In this paper, we study all these…
A 1.5D imprecise terrain is an $x$-monotone polyline with fixed $x$-coordinates, the $y$-coordinate of each vertex is not fixed but is constrained to be in a given vertical interval. A 2.5D imprecise terrain is a triangulation with fixed…
Given an orthogonal polygon $ P $ with $ n $ vertices, the goal of the watchman route problem is finding a path $ S $ of the minimum length in $ P $ such that every point of the polygon $ P $ is visible from at least one of the point of $ S…
We are interested in the problem of guarding simple orthogonal polygons with the minimum number of $ r $-guards. The interior point $ p $ belongs an orthogonal polygon $ P $ is visible from $ r $-guard $ g $, if the minimum area rectangle…
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 $\gamma$…
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…
The art gallery problem enquires about the least number of guards sufficient to ensure that an art gallery, represented by a simple polygon $P$, is fully guarded. Most standard versions of this problem are known to be NP-hard. In 1987,…
The problem of vertex guarding a simple polygon was first studied by Subir K. Ghosh (1987), who presented a polynomial-time $O(\log n)$-approximation algorithm for placing as few guards as possible at vertices of a simple $n$-gon $P$, such…
Guarding a polygon with few guards is an old and well-studied problem in computational geometry. Here we consider the following variant: We assume that the polygon is orthogonal and thin in some sense, and we consider a point $p$ to guard a…
Given is a 1.5D terrain $\mathcal{T}$, i.e., an $x$-monotone polygonal chain in $\mathbb{R}^2$. For a given $2\le k\le n$, our objective is to approximate the largest area or perimeter convex polygon of exactly or at most $k$ vertices…