Abstract
This paper studies the two-dimensional range search problem, and constructs a simple and efficient algorithm based on the Voronoi diagram. In this problem, a set of points and a query range are given, and we want to enumerate all the points which are inside the query range as quickly as possible. In most of the previous researches on this problem, the shape of the query range is restricted to particular ones such as circles, rectangles and triangles, and the improvement on the worst-case performance has been pursued. On the other hand, the algorithm proposed in this paper is designed for a general shape of the query range, and is intended to accomplish a good average-case performance. This performance is actually observed by numerical experiments. We can observe that our algorithm shows the better performance in almost all the cases.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. L. Bentley: Multidimensional binary search trees used for associative searching, Communications of the ACM, vol. 18 (1975) 509–517.
J. L. Bentley, D. F. Stanat, E. H. Williams, Jr.: The complexity of finding fixed-radius near neighbors, Information processing letters, vol. 6,No. 6 (1977) 209–212.
J. L. Bentley, H. A. Maurer: A note on Euclidean near neighbor searching in the plane, Information processing letters, vol. 8, No. 3 (1979) 133–136.
M. de Berg, M. van Kreveld, M. Overmars, O. Schwarzkopf: Computational geometry — algorithms and applications —, Springer-Verlag, Berlin, Heidelberg (1997).
B. Chazelle, R. Cole, F. P. Prepareta, C. Yap: New upper bounds for neighbor searching, Information and control, vol. 68 (1986) 105–124.
H. Edelsbrunner, E. Welzl: Halfplanar range search in linear space and O(n 0.695) query time, Information processing letters, vol. 23 (1986) 289–293.
J. E. Goodman, J. O’Rourke: Handbook of discrete and computational geometry, CRC press, Boca Raton, New York (1997).
J. Matoušek: Geometric range searching, ACM computing survey, vol. 26, No. 4 (1994).
T. Ohya, M. Iri, K. Murota: Improvements of the incremental method for the Voronoi diagram with computational comparison of various algorithms, Journal of operations research society of Japan, vol. 27, No. 4 (1984) 69–97.
A. Okabe, B. Boots, K. Sugihara, S.-N. Chiu: Spatial tessellations —concepts and applications of Voronoi diagrams, second edition, John Wiley & Sons (2000).
F. P. Preparata, M. I. Shamos: Computational geometry — an introduction, Springer-Verlag, New York (1985).
G. Yuval: Finding near neighbours in k-dimensional space, Information processing letters, vol. 3, No. 4, pp. 113–114, March 1975.
C. Böhm, S. Berchtold and D. A. Keim: Searching in high-dimensional spaces — Index structures for improving the performance of multimedia databases, ACM Computing Surveys, vol. 33, No. 3 (2001) 322–373.
E. Chávez, G. Navarro, R. Baeza-Yates and J. L. Marroquín: Searching in metric spaces, ACM Computing Surveys, vol. 33, No. 3 (2001) 273–321.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kanda, T., Sugihara, K. (2003). Two-Dimensional Range Search Based on the Voronoi Diagram. In: Kumar, V., Gavrilova, M.L., Tan, C.J.K., L’Ecuyer, P. (eds) Computational Science and Its Applications — ICCSA 2003. ICCSA 2003. Lecture Notes in Computer Science, vol 2669. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44842-X_79
Download citation
DOI: https://doi.org/10.1007/3-540-44842-X_79
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40156-8
Online ISBN: 978-3-540-44842-6
eBook Packages: Springer Book Archive