Maximum-Width Rainbow-Bisecting Empty Annulus

05/16/2023

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by   Sang Won Bae, et al.

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Given a set of n colored points with k colors in the plane, we study the problem of computing a maximum-width rainbow-bisecting empty annulus (of objects specifically axis-parallel square, axis-parallel rectangle and circle) problem. We call a region rainbow if it contains at least one point of each color. The maximum-width rainbow-bisecting empty annulus problem asks to find an annulus A of a particular shape with maximum possible width such that A does not contain any input points and it bisects the input point set into two parts, each of which is a rainbow. We compute a maximum-width rainbow-bisecting empty axis-parallel square, axis-parallel rectangular and circular annulus in O(n^3) time using O(n) space, in O(k^2n^2log n) time using O(nlog n) space and in O(n^3) time using O(n^2) space respectively.