Given a simple polygon P, we say that two points p, q∈ P see each other if the line segment
pq is contained in P. A set of points G⊆ P is said to guard the polygon P if every point p∈ P …

Handbook of DISCRETE AND COMPUTATIONAL GEOMETRY Page 1 i “K25063” — 2017/9/15
— 18:58 — page 875 — i i i 33 VISIBILITY Joseph O’Rourke INTRODUCTION In a …

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 show that vertex guarding a monotone polygon is NP-hard and construct a constant
factor approximation algorithm for interior guarding monotone polygons. Using this algorithm …

We survey the complexity class $\exists\mathbb {R} $, which captures the complexity of
deciding the existential theory of the reals. The class $\exists\mathbb {R} $ has roots in two …

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 …

The local search framework for obtaining PTASs for NP-hard geometric optimization
problems was introduced, independently, by Chan and Har-Peled [6] and Mustafa and Ray …

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 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 …

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 …