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Floodlight Illumination of Infinite Wedges
"... The floodlight illumination problem asks whether there exists a onetoone 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 p ..."
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The floodlight illumination problem asks whether there exists a onetoone 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 NPhard, closing an open problem posed by Demaine and O’Rourke (CCCG 2001). In fact, we show that the problem is NPcomplete even when αi = α for all 1 ≤ i ≤ n (the uniform case) and θ = � n i=1 αi (the tight case). Key words: illumination, art gallery problem, floodlights, NPcompleteness 1
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"... If P is a set of points in a plane and S is a subset of nonhull points, then T P S denotes the set of all pseudotriangulations in which S vertices are nonpointed. It is shown that the flip graph on T P S pseudotriangulations is connected and no flip edge exists between pseudotriangulations of T P ..."
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If P is a set of points in a plane and S is a subset of nonhull points, then T P S denotes the set of all pseudotriangulations in which S vertices are nonpointed. It is shown that the flip graph on T P S pseudotriangulations is connected and no flip edge exists between pseudotriangulations of T P