Skip to main content
SpringerLink
Log in
Book cover

International Colloquium on Automata, Languages, and Programming

ICALP 1985: Automata, Languages and Programming pp 111–119Cite as

Partitioning point sets in 4 dimensions

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 194))

Abstract

We introduce a new type of partition called a parallel planes partition. We prove there exists a parallel planes partition of any set of n points in 4 dimensions. This partition yields a data structure for the half-space retrieval problem in 4 dimensions; it has linear size and achieves a sublinear query time.

This work was supported in part by NSF grant DCR-84-01633 and by an IBM faculty development award.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D. Avis, Non-Partitionable Point Sets, manuscript, McGill University.

    Google Scholar 

  2. R. Cole, M. Sharir, C. Yap, On k-hulls and Related Problems, STOC, 1984, pp.154–166.

    Google Scholar 

  3. B. Chazelle, L. Guibas, D. Lee, The Power of Geometric Duality, FOCS, 1983, pp.217–225.

    Google Scholar 

  4. D. Dobkin and H. Edelsbrunner, Organizing Points in Two and Three Dimensions, manuscript.

    Google Scholar 

  5. D. Dobkin and H. Edelsbrunner, Space Searching for Intersecting Objects, FOCS, 1984, pp.387–392.

    Google Scholar 

  6. H. Edelsbrunner, private communication.

    Google Scholar 

  7. H. Edelsbrunner and E. Welzl, Halfplane Range Search in Linear Space and O(n 0.695) query time, Tech. Rep. F111, Graz University, 1982.

    Google Scholar 

  8. M. Fredman, The Inherent Complexity of Dynamic Data Structures which Accommodate Range Queries, FOCS, 1980, pp.191–199.

    Google Scholar 

  9. S. Lefschetz, Introduction to Topology, Princeton University Press.

    Google Scholar 

  10. N. Megiddo, Applying Parallel Computation Algorithms in the Design of Serial Algorithms, 4(1983), pp.852–865.

    Google Scholar 

  11. D. Willard, Polygon Retrieval, SIAM J. Comput., 11(1982), pp.149–165.

    Article  Google Scholar 

  12. F. Yao, A 3-Space Partition and its Applications, Proc. 15th STOC, 1983, pp. 258–263.

    Google Scholar 

  13. F. Yao, private communication.

    Google Scholar 

  14. F. Yao, private communication, to appear, with A. Yao, in STOC 85.

    Google Scholar 

  15. I. M. Yaglom and V.G. Boltyanskii, Convex Figures, Holt, Rinehart and Winston, Translation (1961).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Courant Institute of Mathematical Sciences, New York University, 10012, New York, NY

    Richard Cole

Authors
  1. Richard Cole
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Wilfried Brauer

Rights and permissions

Reprints and permissions

Copyright information

© 1985 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Cole, R. (1985). Partitioning point sets in 4 dimensions. In: Brauer, W. (eds) Automata, Languages and Programming. ICALP 1985. Lecture Notes in Computer Science, vol 194. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015736

Download citation

  • DOI: https://doi.org/10.1007/BFb0015736

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15650-5

  • Online ISBN: 978-3-540-39557-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation