Maximum-width rainbow-bisecting empty annulus

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...

Full description

Saved in:

Bibliographic Details
Published in:	Computational geometry : theory and applications Vol. 120; p. 102088
Main Authors:	Bae, Sang Won, Banerjee, Sandip, Baral, Arpita, Mahapatra, Priya Ranjan Sinha, Yoon, Sang Duk
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01.06.2024
Subjects:	Geometric covering L shaped corridor Polynomial-time algorithms Rainbow-bisecting annulus Rainbow-bisecting annulus Geometric covering L shaped corridor Polynomial-time algorithms
ISSN:	0925-7721
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	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.
ISSN:	0925-7721
DOI:	10.1016/j.comgeo.2024.102088