Two-Floodlight Illumination of Convex Polygons

Art Gallery and Illumination Problems

How many guards are necessary, and how many are sufficient to patrol the paintings and works of art in an art gallery with n walls? This wonderfully na¨ıve question of combinatorial geometry has, since its formulation, stimulated an increasing number of of papers and surveys. In 1987, J. O'Rourke published his book Art Gallery Theorems and Algorithms which has further fueled this area of resear...

The Complexity of Illuminating Polygons by -Flood-Lights

The Floodlight Illumination Problem (FIP) is the determination of the minimum number of vertex-lights required to illuminate a given polygon. We show that FIP for simple polygon is NP-hard for any xed in the range 0 < 360 0. We further show that FIP for simple polygons is NP-Hard even when-lights are required to be ush with the edges of the polygon. Our technique is based on the construction of...

Continuous Surveillance of Points by rotating Floodlights

Let P and F be sets of n ≥ 2 and m ≥ 2 points in a plane, respectively. We study the problem of finding the minimum angle α ∈ [2π/m, 2π] such that one can install at each point of F a stationary rotating floodlight with illumination angle α, initially oriented in a suitable direction, in such a way that, at all times, every target point of P is illuminated by at least one floodlight. All floodl...

Two Applications of Point Matching

The two following problems can be solved by a reduction to a minimum-weight bipartite matching problem (or a related network flow problem): a) Floodlight illumination: We are given n infinite wedges (sectors, spotlights) that can cover the whole plane when placed at the origin. They are to be assigned to n given locations (in arbitrary order, but without rotation) such that they still cover the...

Illuminating convex polygonswith vertex floodlight