Floodlight illumination of infinite wedges

Floodlight illumination of infinite wedges

The floodlight illumination problem asks whether there exists a one-to-one placement of n floodlights illuminating infinite wedges of angles α1, . . . , αn at n sites p1, . . . , pn in a plane such that a given infinite wedge W of angle θ located at point q is completely illuminated by the floodlights. We prove that this problem is NP-hard, closing an open problem from 2001 [6]. In fact, we sho...

Two-Floodlight Illumination of Convex Polygons

A floodlight of size α is a light source that projects light in a cone of size α . In this paper we study the problem of illuminating a convex polygon using floodlights. We give an O(n 2 ) time algorithm to find an optimal pair of floodlights to illuminate a convex polygon P with n vertices; that is a pair of floodlights to illuminate a convex polygon in such a way that the sum of their sizes i...

Semi-Infinite Wedges and Vertex Operators

The level 1 highest weight modules of the quantum affine algebra Uq(ŝln) can be described as spaces of certain semi-infinite wedges. Using a q-antisymmetrization procedure, these semi-infinite wedges can be realized inside an infinite tensor product of evaluation modules. This realization gives rise to simple descriptions of vertex operators and (up to a scalar function) their compositions. 1 R...

The Floodlight Problem

Given three angles summing to 2 , given n points in the plane and a tripartition k1 + k2 + k3 = n, we can tripartition the plane into three wedges of the given angles so that the i-th wedge contains ki of the points. This new result on dissecting point sets is used to prove that lights of speci ed angles not exceeding can be placed at n xed points in the plane to illuminate the entire plane if ...

Illuminating convex polygonswith vertex floodlight