Acta Informatica

, Volume 17, Issue 3, pp 245–265

Deleting the root of a heap

  • Ernst E. Doberkat


The average behavior of the familiar algorithm for root deletion is considered, when every heap has the same probability to occur. The analysis centers around the notion of a viable path in the tree representation, i.e. such a path the label which replaces the label of the root may be allowed to travel when the heap is reconstructed. In case the size of the heap is a power of 2 it is shown that both the expected number of comparisons and of interchanges are asymptotically equal to the respective numbers in the worst case.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aho, A.V., Hopcroft, J.E., Ullman, J.D.: The Design and Analysis of Computer Algorithms. Reading: Addison-Wesley, MA 1974Google Scholar
  2. 2.
    Bailey, W.N.: Generalized Hypergeometric Series. Cambridge: University Press 1935Google Scholar
  3. 3.
    Bender, E.A.: Asymptotic Methods in Enumeration. SIAM Review 16 (1974) 485–515Google Scholar
  4. 4.
    Doberkat, E.E.: Some Observations on the Average Performance of Heapsort — Preliminary Report. 21st IEEE FOCS, Syracuse, N.Y. 1980, 229–237Google Scholar
  5. 5.
    Doberkat, E.E.: Inserting a New Element into a Heap. BIT 21 (1981) 255–269Google Scholar
  6. 6.
    Doberkat, E.E.: Continuous Models that are Equivalent to Randomness for the Analysis of Many Sorting Algorithms. Preprint 1981, submitted for publicationGoogle Scholar
  7. 7.
    Habermann, A.N.: Introduction to Operating System Design. Chicago: Science Research Associates 1976Google Scholar
  8. 8.
    Hansen, E.R.: A Table of Series and Products. Prentice-Hall: Englewood Cliffs 1975Google Scholar
  9. 9.
    Knuth, D.E.: The Art of Computer Programming — Vol. 3, Sorting and Searching. Reading: Addison-Wesley, MA 1973Google Scholar
  10. 10.
    Rudin, W.: Real and Complex Analysis. New Delhi: Tata McGraw Hill 1974 (second edition)Google Scholar
  11. 11.
    Whittaker, E.T., Watson, G.N.: A Course of Modern Analysis (Fourth Edition). Cambridge: University Press 1927Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Ernst E. Doberkat
    • 1
  1. 1.Department of Mathematics and Computer ScienceClarkson College of TechnologyPotsdamUSA

Personalised recommendations