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ISPRS Int. J. Geo-Inf. 2017, 6(3), 82; doi:10.3390/ijgi6030082

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

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.
Academic Editor: Wolfgang Kainz
Received: 1 February 2017 / Revised: 9 March 2017 / Accepted: 13 March 2017 / Published: 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
Keywords: spatial data structures; point location queries; nearest point queries; selectivity estimation spatial data structures; point location queries; nearest point queries; selectivity estimation
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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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