Skip to main content
SpringerLink
Log in

Computing a Closest Point to a Query Hyperplane in Three and Higher Dimensions

  • Conference paper
  • First Online:
Computational Science and Its Applications — ICCSA 2003 (ICCSA 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2669))

Included in the following conference series:

Abstract

Given a set S of n points in E d (d ≥ 3), we consider the problem of computing a closest point to a query hyperplane Q. For d = 3, we report an algorithm whose preprocessing time is in O(n 1+ɛ), space complexity is in O(n log n) and query time is in O(n 2/3+ɛ). For d > 3, we adopt a different approach and propose an algorithm which has a query time in O(d log n), in an amortized sense, under a rather strong assumption that we explain in the paper, with O(n d+k) preprocessing space and, O(n d+1+k) preprocessing time, both in an expected sense, for some k > 0.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

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.

References

  1. R. Cole and C. Yap, Geometric retrieval problems, Proc. IEEE 24th Symp. on Foundations of Computer Science, pp 112–121, 1983.

    Google Scholar 

  2. H. Edelsbrunner and L. J. Guibas, Topologically sweeping an arrangement, J. Comput. Syst. Sci., Vol. 38, pp 165–194, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  3. D. G. Kirkpatrick, Optimal search in planar subdivisions, SIAM J. Comput., Vol. 12(1), pp 28–35, 1983.

    Article  MATH  MathSciNet  Google Scholar 

  4. D. T. Lee and Y. T. Ching, The power of geometric duality revisited, IPL, Vol. 21, pp 117–122, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  5. Asish Mukhopadhyay, Using simplicial partitions to determine the closest point to a query line, in Pattern Recognition Letters, to appear.

    Google Scholar 

  6. S. Meiser, Point location in arrangements of hyperplanes, Information and Computation, Vol. 106, pp 286–303, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  7. P. Mitra, Finding the closest point to a query line, Snapshots in Computational Geometry (Editor G. Toussaint), Vol II, pp 53–63, 1992.

    Google Scholar 

  8. P. Mitra and B. B. Chaudhuri, Efficiently computing tthe closest point to a query line, Pattern Recognition Letters, Vol 19, pp 1027–1035, 1998.

    Article  MATH  Google Scholar 

  9. J. Matoušek, Efficient partition trees, Discrete and Computational Geometry, Vol. 8, pp 315–334, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  10. Mark de Berg, Marc van Kreveld, Mark Overmarks, Otfried Schwarzkopf, Computational Geometry: Algorithms and Applications, Second edition, Springer Verlag, 2001.

    Google Scholar 

  11. Franco P. Preparata, M. I. Shamos, Computational Geometry: An Introduction, Springer-Verlag, 2nd edition, 1990.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. NIMC, Alipore, Calcutta, India

    Pinaki Mitra

  2. School of Computer Science, University of Windsor, Windsor, Canada

    Asish Mukhopadhyay

Authors
  1. Pinaki Mitra
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Asish Mukhopadhyay
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Army High Performance Computing Research Center, USA University of Minessota Department of Computer Science and Engineering, MN, 55455, USA

    Vipin Kumar

  2. Department of Computer Science, University of Calgary, Calgary, AB, T2N1N4, Canada

    Marina L. Gavrilova

  3. Heuchera Technologies Inc., 122 9251-8Yonge Street, Richmond Hill, ON, Canada, L4C 9T3

    Chih Jeng Kenneth Tan

  4. School of Computer Science, The Queen’s University of Belfast, Belfast, BT7 1NN, Northern Ireland UK

    Chih Jeng Kenneth Tan

  5. Département d’informatique et de recherche opérationelle Montréal, Université de Montréal, Québec, H3C 3J7, Canada

    Pierre L’Ecuyer

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Mitra, P., Mukhopadhyay, A. (2003). Computing a Closest Point to a Query Hyperplane in Three and Higher Dimensions. 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_80

Download citation

  • DOI: https://doi.org/10.1007/3-540-44842-X_80

  • 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

Publish with us

Policies and ethics

Search

Navigation