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...

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Veröffentlicht in:	Computational geometry : theory and applications Jg. 120; S. 102088
Hauptverfasser:	Bae, Sang Won, Banerjee, Sandip, Baral, Arpita, Mahapatra, Priya Ranjan Sinha, Yoon, Sang Duk
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Elsevier B.V 01.06.2024
Schlagworte:	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
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Zusammenfassung:	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