Rheinische Friedrich - Wilhelms - Universität Bonn
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چکیده
Given n point sites in the plane each painted in one of k colors, the region of a c-colored site p in the Farthest Color Voronoi Diagram (FCVD) contains all points of the plane for which c is the farthest color and p the nearest c-colored site. This novel structure generalizes both the standard Voronoi diagram (k = 1) and the farthest site Voronoi diagram (k = n). We show that the FCVD has structural complexity Θ(nk) if k ≤ n 2 , and we provide an O(nα(k) log k) algorithm for computing the FCVD. We call a set color-spanning if it contains at least one point of each color. From the FCVD, we can quickly determine the smallest color-spanning circle. Moreover, we present algorithms for computing a color-spanning axis parallel rectangle of minimum area or perimeter in time O(n(n−k) log k) and for finding the narrowest color-spanning strip in time O(nα(k) log k).
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تاریخ انتشار 2006