How to Advance on a Stairway by Coin Flippings

  • Helmut Prodinger
Chapter

Abstract

Assume that N persons want to advance on a stairway. The rule is as follows: They start at level 1. The k ≥ 1 persons who advanced to the level j flip a (fair) coin; the persons with the “1” advance; the others (with a “0”) die. However, there is a demon supervising the game. Usually, he “consumes” one of the survivors. But, with a probability p, he resigns and does not interfere. (The demon can only interfere at levels 2 or larger.) The question is, how far can the party advance, on the average?

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Flajolet, P. “Approximate Counting: A Detailed Analysis.” BIT, Vol. 25 (1985): pp. 113–134.MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    Flajolet, P. and Sedgewick, R. “Digital Search Trees Revisited.” SIAM J. Comput., Vol. 15 (1986): pp. 748–767.MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    Kirschenhofer, P. and Prodinger, H. “Approximate Counting: An Alternative Approach.” RAIRO Informatique Théorique et Applications. Vol. 25 (1991): pp. 43–48.MathSciNetMATHGoogle Scholar
  4. [4]
    Knuth, D.E. The Art of Computer Programming. Vol. 3, Addison-Wesley, Reading, MA, 1973.Google Scholar
  5. [5]
    Mahmoud, H.M. Evolution of Random Search Trees. Wiley-Interscience Series in Discrete Mathematics and Optimization, New York, 1992.MATHGoogle Scholar
  6. [6]
    Nörlund, N.E. Vorlesungen über Differenzenrechnung. Chelsea, New York, 1954.Google Scholar
  7. [7]
    Prodinger, H. “Hypothetic Analyses: Approximate Counting in the Style of Knuth, Path length in the Style of Flajolet.” Theoret. Comput. Sci., Vol. 100 (1992): pp. 243–251.MathSciNetMATHCrossRefGoogle Scholar
  8. [8]
    Schmid, U. “Analyse von Collision-Resolution Algorithmen in Random-Access Systemen mit dominanten Übertragungskanälen.” Dissertation, TU Wien, 1986, published as “On a Tree Collision Resolution Algorithm in Presence of Capture.” RAIRO Informatique Théorique et Applications. Vol. 26 (1992): pp. 163–197.MATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1993

Authors and Affiliations

  • Helmut Prodinger

There are no affiliations available

Personalised recommendations