• Journal of KIISE
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• v.44 no.3
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• pp.246-252
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• 2017

In this paper, we present an algorithm that computes a minimum-width color spanning axis-parallel rectangular annulus. A rectangular annulus is a closed region between a rectangle and its offset, and it is thus bounded by two rectangles called its outer and inner rectangles. The width of a rectangular annulus is determined by the distance between its outer and inner rectangles. Given n points in the plane each of which has one of the prescribed k colors, we call a rectangular annulus color spanning if it contains at least one point for each of the k colors. Prior to this work, there was no known exact algorithm that computes a minimum-width color-spanning rectangular annulus. Our algorithm is the first to solve this problem and it runs efficiently in $O((n-k)^3nlogn)$ time.