Finding the Maximum Empty Axis-Parallel Rectangular Annulus

An annulus is basically a ring-shaped region between two concentric disks on the same plane. However, it can be defined on any other geometrical shapes, for example, a rectangular annulus is defined as the area between two rectangles with one rectangle enclosing the other. The area of the annulus is...

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Bibliographic Details
Published inCombinatorial Image Analysis Vol. 12148; pp. 139 - 146
Main Authors Paul, Raina, Sarkar, Apurba, Biswas, Arindam
Format Book Chapter
LanguageEnglish
Published Switzerland Springer International Publishing AG 2020
Springer International Publishing
SeriesLecture Notes in Computer Science
Subjects
Annulus
Axis-parallel annulus
Rectangular annulus
Online AccessGet full text
ISBN9783030510015
3030510018
ISSN0302-9743
1611-3349
DOI10.1007/978-3-030-51002-2_10

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Summary:An annulus is basically a ring-shaped region between two concentric disks on the same plane. However, it can be defined on any other geometrical shapes, for example, a rectangular annulus is defined as the area between two rectangles with one rectangle enclosing the other. The area of the annulus is the area of the region between the two shapes. An axis-parallel rectangular annulus is an annulus where the sides of the rectangles are parallel to the co-ordinate axes. This paper presents a combinatorial technique to find the largest empty axis-parallel rectangular annulus from a given set of n points and runs in $$O(n\log n)$$ time. It uses two balanced binary search trees to store the points and reduces the complexity of the existing algorithm in the literature.
Bibliography:Original Abstract: An annulus is basically a ring-shaped region between two concentric disks on the same plane. However, it can be defined on any other geometrical shapes, for example, a rectangular annulus is defined as the area between two rectangles with one rectangle enclosing the other. The area of the annulus is the area of the region between the two shapes. An axis-parallel rectangular annulus is an annulus where the sides of the rectangles are parallel to the co-ordinate axes. This paper presents a combinatorial technique to find the largest empty axis-parallel rectangular annulus from a given set of n points and runs in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(n\log n)$$\end{document} time. It uses two balanced binary search trees to store the points and reduces the complexity of the existing algorithm in the literature.
ISBN:9783030510015
3030510018
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-030-51002-2_10