Finding the maximum with linear error probabilities: a sequential analysis approach

  • Guy Louchard
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 900)


Assume that n players are represented by n reals, uniformly distributed over the unit interval.

We assume that the error probability of a comparison game between two players depends linearly on the distance between the players. Using sequential analysis approach, we present an algorithm to estimate the maximum ξ of the players with an error less than ε.

Mean cost, variance and centered moments generating function are analyzed.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. Adler, P. Gemmell, M. Harchol, R.M. Karp and Cl. Kenyon Selection in the Presence of Noise: The Design of Playoff Systems Proc. SODA 1994, San Francisco.Google Scholar
  2. 2.
    D.A. Darling and J.F. Siegert The First Passage Problem for a Continuous Markov Process An. Math. Stat. 1953, 624–639.Google Scholar
  3. 3.
    U. Feige, D. Peleg, P. Raghavan and E. Upfal Computing with Unreliable Information. In Symposium on Theory of Computing, 1990, 128–137.Google Scholar
  4. 4.
    B.K. Gosh and P.K. Sen Handbook of Sequential Analysis. Marcel Dekker, 1991.Google Scholar
  5. 5.
    G. Louchard, R. Schott Probabilistic Analysis of Some Distributed Algorithms. Wiley, Random Structures and Algorithms 2, 2, 1991, 151–186.Google Scholar
  6. 6.
    G. Louchard Finding the maximum with linear error probabilities: a sequential analysis approach, Département d'Informatique, TR-297, 1994.Google Scholar
  7. 7.
    V.V. Petrov Sums of Independent Random Variables Ergebnisse der Mathematik und ihrer Grenzgebiete. Band 82, Springer-Verlag, 1975.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Guy Louchard
    • 1
  1. 1.Département d'InformatiqueUniversité Libre de BruxellesBruxellesBelgique

Personalised recommendations