Lower bounds for problems defined by polynomial inequalities

  • Jerzy W. Jaromczyk
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 117)


We have offered the method to study the lower bounds in a reasonable wide class of decision trees.

On the other hand we have shown that for certain problems wider classes decision trees are sometimes profitless. We believe that demonstrated approach can be helpful while considering problems in Computational Geometry.

At the end it is worth noticing that a case in which all the polynomials of the description are linear seems to be of the special interest.


Decision Tree Convex Hull Convex Polygon Identity Property Complete Proof 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Avis, D., Comments on a lower bound for convex hull determination. Inf. Proc. Let., 11 (1980), 126.Google Scholar
  2. 2.
    Jaromczyk, J., W., Linear decision trees are too weak for convex hull problem. to appear in Inf. Proc. Let.Google Scholar
  3. 3.
    Jaromczyk, J., W., A note on Rabin's complete proof notion (preliminary version). IInf UW Reports, 102 (1981).Google Scholar
  4. 4.
    Jaromczyk, J., W., to appear.Google Scholar
  5. 5.
    Kendig, K., Elementary Algebraic Geometry. Springer Verlag, New York, 1977.Google Scholar
  6. 6.
    Rabin, M., O., Proving simultaneous positivity of linear forms. J. Comp. Sys. Sci., 6 (1972), 639–650.Google Scholar
  7. 7.
    Snir, M., communicated to me by Peter van Emde Boas.Google Scholar
  8. 8.
    Spira, P., M., Complete linear proofs of systems of linear inequalities. J. Comp. Sys. Sci., 6 (1972), 205–216.Google Scholar
  9. 9.
    van der Waerden, B. L., Einführung in die algebraische Geometrie. Springer Verlag, Berlin, 1973.Google Scholar
  10. 10.
    Yao, A., C., A lower bound to finding convex hulls. Report STAN-CS-79-733, April 1979.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • Jerzy W. Jaromczyk
    • 1
  1. 1.Institute of InformaticsWarsaw UniversityWarsawPoland

Personalised recommendations