Skip to main content
SpringerLink
Log in

Lower bounds for polygon simplicity testing and other problems

  • Communications
  • Conference paper
  • First Online:
Mathematical Foundations of Computer Science 1984 (MFCS 1984)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 176))

Abstract

The new non-trivial lower bounds of time complexity for some problems of computational geometry such as:

  1. -

    polygon simplicity testing (computational version)

  2. -

    finding diameter of a set of points in R2

  3. -

    finding maximal distance between two sets of points in R2

are derived. Some attractive geometrical constructions e.g., a curve with a constant width are used while proving the lower bounds.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Avis, D., Lower bounds for geometric problems. Allerton Conference, October 1980.

    Google Scholar 

  2. Ben-Or, M., Lower bounds for algebraic computation trees, Proc. of 15-th STOC, Boston, 1983, 80–86.

    Google Scholar 

  3. Boyce, J.E., Dobkin, D.P., Drysdale, R.L., Guibas, L.J., Finding extremal polygons, Proc. of 14-th STOC, 1982, 282–289.

    Google Scholar 

  4. Edelsbrunner, H., Bulletin of EATCS, No.21, October 1983.

    Google Scholar 

  5. Jaglom, I.M., Boltianski, V.G., Convex Figures, W-wa 1955 (polish)

    Google Scholar 

  6. Jaromczyk, J.W., A complexity bounds and euclidean space partitionig, Coll. on Alg., Comb. & Logic, Györ-Hungary, September 83.

    Google Scholar 

  7. Milnor, J., On the betti numbers of real algebraic varieties, Proc. AMS 15, 1964, 275–280.

    Google Scholar 

  8. Morávek, J., A lokalization problem in geometry and complexity of discrete programming, Kybernetika 8(6), 1972, 498–516.

    Google Scholar 

  9. Shamos, M.I., Computational geometry, Ph.D.Thesis, Yale Uni. 1978.

    Google Scholar 

  10. Steele, J.M., Yao, A.C., Lower bounds for algebraic decision trees, J. Algorithms 3, 1982, 1–8.

    Google Scholar 

  11. Toussaint, G.T., Pattern recognition and geometrical complexity, Conference on Pattern Recognition, 1980, 1324–1347.

    Google Scholar 

  12. Toussaint, G.T., McAlear, J.A., A simple O(nlogn) algorithm for Tech.Rep.No.SOCS-82-6, March 1982, McGill Uni.

    Google Scholar 

  13. Yao, A.C., Rivest, R., On the polyhedral decision problem, SIAM J. on Comput. 9(2), 1980), 343–347.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Informatics, Warsaw University, PKiN VIII p., 00-901, Warsaw, Poland

    Jerzy W. Jaromczyk

Authors
  1. Jerzy W. Jaromczyk
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

M. P. Chytil V. Koubek

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Jaromczyk, J.W. (1984). Lower bounds for polygon simplicity testing and other problems. In: Chytil, M.P., Koubek, V. (eds) Mathematical Foundations of Computer Science 1984. MFCS 1984. Lecture Notes in Computer Science, vol 176. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030315

Download citation

  • DOI: https://doi.org/10.1007/BFb0030315

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13372-8

  • Online ISBN: 978-3-540-38929-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation