Maximum-width rainbow-bisecting empty annulus - Bae, Sang Won; Banerjee, Sandip; Baral, Arpita; Mahapatra, Priya Ranjan Sinha; Yoon, Sang Duk (Computational geometry : theory and applications, 2024)
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(n3) time using O(n) space, in O(k2n2log⁡n) time using O(nlog⁡n) space and in O(n3) time using O(n2) space respectively.