A Dynamic Data Structure to Efficiently Find the Points below a Line and Estimate Their Number

A basic question in computational geometry is how to find the relationship between a set of points and a line in a real plane. In this paper, we present multidimensional data structures for N points that allow answering the following queries for any given input line: (1) estimate in O ( log N )...

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Bibliographic Details
Main Authors:	Bart Kuijpers, Peter Z. Revesz
Format:	Article
Language:	English
Published:	MDPI AG 2017-03-01
Series:	ISPRS International Journal of Geo-Information
Subjects:	spatial data structures point location queries nearest point queries selectivity estimation
Online Access:	http://www.mdpi.com/2220-9964/6/3/82

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spelling	doaj-73b91029869c44b1abccab62d80afc262020-11-24T23:26:30ZengMDPI AGISPRS International Journal of Geo-Information2220-99642017-03-01638210.3390/ijgi6030082ijgi6030082A Dynamic Data Structure to Efficiently Find the Points below a Line and Estimate Their NumberBart Kuijpers0Peter Z. Revesz1UHasselt–Hasselt University and transnational University Limburg, Databases and Theoretical Computer Science Research Group, Agoralaan, Gebouw D, Diepenbeek 3590, BelgiumDepartment of Computer Science & Engineering, University of Nebraska-Lincoln, 256 Avery Hall, 1144 T Street, Lincoln, NE 68588-0115, USAA basic question in computational geometry is how to find the relationship between a set of points and a line in a real plane. In this paper, we present multidimensional data structures for N points that allow answering the following queries for any given input line: (1) estimate in O ( log N ) time the number of points below the line; (2) return in O ( log N + k ) time the k ≤ N points that are below the line; and (3) return in O ( log N ) time the point that is closest to the line. We illustrate the utility of this computational question with GIS applications in air defense and traffic control.http://www.mdpi.com/2220-9964/6/3/82spatial data structurespoint location queriesnearest point queriesselectivity estimation
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Bart Kuijpers Peter Z. Revesz
spellingShingle	Bart Kuijpers Peter Z. Revesz A Dynamic Data Structure to Efficiently Find the Points below a Line and Estimate Their Number ISPRS International Journal of Geo-Information spatial data structures point location queries nearest point queries selectivity estimation
author_facet	Bart Kuijpers Peter Z. Revesz
author_sort	Bart Kuijpers
title	A Dynamic Data Structure to Efficiently Find the Points below a Line and Estimate Their Number
title_short	A Dynamic Data Structure to Efficiently Find the Points below a Line and Estimate Their Number
title_full	A Dynamic Data Structure to Efficiently Find the Points below a Line and Estimate Their Number
title_fullStr	A Dynamic Data Structure to Efficiently Find the Points below a Line and Estimate Their Number
title_full_unstemmed	A Dynamic Data Structure to Efficiently Find the Points below a Line and Estimate Their Number
title_sort	dynamic data structure to efficiently find the points below a line and estimate their number
publisher	MDPI AG
series	ISPRS International Journal of Geo-Information
issn	2220-9964
publishDate	2017-03-01
description	A basic question in computational geometry is how to find the relationship between a set of points and a line in a real plane. In this paper, we present multidimensional data structures for N points that allow answering the following queries for any given input line: (1) estimate in O ( log N ) time the number of points below the line; (2) return in O ( log N + k ) time the k ≤ N points that are below the line; and (3) return in O ( log N ) time the point that is closest to the line. We illustrate the utility of this computational question with GIS applications in air defense and traffic control.
topic	spatial data structures point location queries nearest point queries selectivity estimation
url	http://www.mdpi.com/2220-9964/6/3/82
work_keys_str_mv	AT bartkuijpers adynamicdatastructuretoefficientlyfindthepointsbelowalineandestimatetheirnumber AT peterzrevesz adynamicdatastructuretoefficientlyfindthepointsbelowalineandestimatetheirnumber AT bartkuijpers dynamicdatastructuretoefficientlyfindthepointsbelowalineandestimatetheirnumber AT peterzrevesz dynamicdatastructuretoefficientlyfindthepointsbelowalineandestimatetheirnumber
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A Dynamic Data Structure to Efficiently Find the Points below a Line and Estimate Their Number

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