Altitude Terrain Guarding and Guarding Uni-Monotone Polygons

A 4-Approximation Algorithm for Guarding 1.5-Dimensional Terrains

In the 1.5-dimensional terrain guarding problem we are given as input an x-monotone chain (the terrain) and asked for the minimum set of guards (points on the terrain) such that every point on the terrain is seen by at least one guard. It has recently been shown that the 1.5-dimensional terrain guarding problem is approximable to within a constant factor [3,7], though no attempt has been made t...

Exact Algorithms for Terrain Guarding

Given a 1.5-dimensional terrain T , also known as an x-monotone polygonal chain, the Terrain Guarding problem seeks a set of points of minimum size on T that guards all of the points on T . Here, we say that a point p guards a point q if no point of the line segment pq is strictly below T . The Terrain Guarding problem has been extensively studied for over 20 years. In 2005 it was already estab...

Guarding the Vertices of an Orthogonal Terrain using Vertex Guards

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 terrain with the minimum number of reflex vertices.

Approximate Guarding of Monotone and Re tilinear Polygons

Optimal guarding of polygons and monotone chains

In this paper we study several problems concerning the guarding of a polygon or a x-monotone polygonal chain P with n vertices from a set of points lying on it. Our results are: (1) An O(n logn) time sequential algorithm for computing the shortest guarding boundary chain of a polygon P. (2) An O(n logn) time sequential algorithm for computing the smallest set of consecutive edges guarding a pol...