Guarding galleries and terrains

Let P be a polygon with n vertices. We say that two points of P see each other if the line segment connecting them lies inside (the closure of) P. In this paper we present efficient approximation algorithms for finding the smallest set G of points of P so that each point of P is seen by at least one point of G, and the points of G are constrained to be belong to the set of vertices of an arbitrarily dense grid. We also present similar algorithms for terrains and polygons with holes.

• Type: Journal
• Year: 2006
• Where: IPL
• Authors: Alon Efrat, Sariel Har-Peled
• Keywords: Efficient Approximation, IPL 2006, Line Segment, Polygons