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

1,* and
1
UHasselt–Hasselt University and transnational University Limburg, Databases and Theoretical Computer Science Research Group, Agoralaan, Gebouw D, Diepenbeek 3590, Belgium
2
Department of Computer Science & Engineering, University of Nebraska-Lincoln, 256 Avery Hall, 1144 T Street, Lincoln, NE 68588-0115, USA
*
Author to whom correspondence should be addressed.
ISPRS Int. J. Geo-Inf. 2017, 6(3), 82; https://doi.org/10.3390/ijgi6030082
Received: 1 February 2017 / Revised: 9 March 2017 / Accepted: 13 March 2017 / Published: 15 March 2017
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PDF [525 KB, uploaded 15 March 2017]
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# Abstract

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. View Full-Text
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

MDPI and ACS Style

Kuijpers, B.; Revesz, P.Z. A Dynamic Data Structure to Efficiently Find the Points below a Line and Estimate Their Number. ISPRS Int. J. Geo-Inf. 2017, 6, 82.

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