Skip to main content

Simplex Range Searching and k Nearest Neighbors of a Line Segment in 2D

  • Conference paper
  • First Online:
Algorithm Theory — SWAT 2002 (SWAT 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2368))

Included in the following conference series:

  • 776 Accesses

Abstract

We present an efficient algorithm for finding k nearest neighbours of a query line segment among a set of points distributed arbitrarily on a two dimensional plane. For solving the above, we improved simplex range searching technique in 2D. Given a set of n points, we preprocess them to create a data structure using O(n 2) time and space, which reports the number of points inside a query triangular region Δ in O(logn) time. The members of P inside Δ can be reported in O(log2 n + κ) time, where κ is the size of the output. Finally, this technique is used to find k nearest neighbors of a query straight line segment in O(log2 n + k) time.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. P. K. Agarwal, M. de Berg, J. Matousek, and O. Schwartzkopf, Constructing levels in arrangement and higher order Voronoi diagram, SIAM J. Computing, vol. 27, pp. 654–667, 1998.

    Article  MATH  Google Scholar 

  2. P. K. Agarwal and J. Matousek, Dynamic half-space range reporting and its applications, Algorithmica, vol. 13, pp. 325–345, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  3. S. Bespamyatnikh and J. Snoeyink, Queries with segments in Voronoi diagram, Computational Geometry-Theory and Applications, vol. 16, pp. 23–33, 2000.

    MATH  MathSciNet  Google Scholar 

  4. T. M. Chan, Random sampling, halfspace range reporting, and construction of (≤ k)-levels in three dimension, SIAM J. Computing, vol. 30, pp. 561–575, 2000.

    Article  MATH  Google Scholar 

  5. R. Cole, Searching and storing similar lists, Journal of Algorithms, vol. 7, pp. 202–230, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  6. B. Chazelle, M. Sharir and E. Welzl, Quasi-optimal upper bounds for simplex range searching and new zone theorems, Algorithmica, vol. 8, pp. 407–429, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  7. R. Cole and C. K. Yap, Geometric retrieval problems, Information and Control, pp. 39–57, 1984.

    Google Scholar 

  8. H. Edelsbrunner, Algorithms in Combinatorial Geometry, Springer, Berlin, 1987.

    MATH  Google Scholar 

  9. H. Edelsbrunner and E. Welzl, Halfplanar range search in linear space and O(n .695) query time, Information Processing Letters, vol. 23, pp. 289–293, 1986.

    Article  MATH  Google Scholar 

  10. D. T. Lee and Y. T. Ching, The power of geometric duality revisited, Information Processing Letters, vol. 21, pp. 117–122, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  11. J. Matousek, Range searching with efficient hierarchical cutting, Proc. 8th. Annual Symp. on Computational Geometry, pp. 276–285, 1992.

    Google Scholar 

  12. S. C. Nandy, An efficient k-nearest neighbors searching algorithm for a query line, Proc. 6th. Annual Int. Conf. on Computing and Combinatorics, LNCS-1858, pp. 291–298, 2000.

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Goswami, P.P., Das, S., Nandy, S.C. (2002). Simplex Range Searching and k Nearest Neighbors of a Line Segment in 2D. In: Penttonen, M., Schmidt, E.M. (eds) Algorithm Theory — SWAT 2002. SWAT 2002. Lecture Notes in Computer Science, vol 2368. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45471-3_8

Download citation

  • DOI: https://doi.org/10.1007/3-540-45471-3_8

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43866-3

  • Online ISBN: 978-3-540-45471-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics