# Showing papers on "Illumination problem published in 1998"

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TL;DR: The technique of unfolding a polygonal billiard table is used in this article to answer certain questions concerning the illumination problem, the main problem addressed is how many point obstacles would suffice to block any billiard path between two points of the polygon.

Abstract: The technique of unfolding a polygonal billiard table is used to answer certain questions concerning the illumination problem The main problem addressed is how many point obstacles would suffice to block any billiard path between two points of the polygon The answer can then be generalized from point obstacles to small ∈-neighborhoods of points

22 citations

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09 Dec 1998

TL;DR: This paper shows that the stage illumination problem, which uses floodlights for illuminating a stage, is NP-complete even with some restrictions.

Abstract: The stage illumination problem presented by Urrutia in 1992 is one of illumination problems, which uses floodlights for illuminating a stage. The problem asks whether or not it is possible to rotate given floodlights around their apexes so as to obtain a final configuration such that a given stage is completely illuminated. The problem for finding a polynomial time algorithm for this problem or proving NP-hardness of this problem was open. This paper shows that it is NP-complete even with some restrictions.

8 citations

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01 May 1998

TL;DR: In this article, the authors consider a horizontal road illuminated by two lights, where P i is the illumination power and h i the height of a lamp, and the coordinates of the lamps are (0, h 1) and (s, h 2 ) wheres is the horizontal distance between the two light sources.

Abstract: In this article we consider a horizontal road illuminated by two lights, where P i is the illumination power and h i the height of a lamp. The coordinates of the lamps are (0, h 1) and (s, h 2 ) wheres is the horizontal distance between the two light sources. Let X = (x, 0) be a point on the road somewhere between the two lights. In this chapter we will look for a point X which is minimally illuminated. In Figure 3.1 we have made a sketch of the situation we will refer to later in this chapter.

8 citations