In this paper, we present approximation algorithms for minimum vertex and edge guard
problems for polygons with or without holes with a total of n vertices. For simple polygons …

A set G of points on a terrain, also known as an x-monotone polygonal chain, is said to
guard the terrain if every point on the terrain is seen by a point in G. Two points on the terrain …

We obtain a polynomial time approximation scheme for the terrain guarding problem
improving upon several recent constant factor approximations. Our algorithm is a local …

Approximation Algorithms for Art Gallery Problems in Polygons and Terrains Page 1
Approximation Algorithms for Art Gallery Problems in Polygons and Terrains Subir Kumar Ghosh …

In the NP-hard continuous 1.5 D 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 …

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 …

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 …

We obtain a polynomial time approximation scheme for the terrain guarding problem
improving upon several recent constant factor approximations. Our algorithm is a local …

We study a generalization of the Set Cover problem called the\emph {Partial Set Cover} in
the context of geometric set systems. The input to this problem is a set system $(X,\mathcal …

Several algorithms with an approximation guarantee of $ O (\log n) $ are known for the Set
Cover problem, where $ n $ is the number of elements. We study a generalization of the Set …