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A case study in comparison based complexity: Finding the nearest value(s)

  • Walter Cunto
  • J. Ian Munro
  • Patricio V. Poblete
Session 1 Invited Presentation
Part of the Lecture Notes in Computer Science book series (LNCS, volume 519)

Abstract

It is shown that 5n/4 plus-minus lower order terms comparisons on average are necessary and sufficient to solve the problem of finding the values of ranks immediately above and below a specified element x in a set X of size n>1. When x turns out to be the median of X, 1.5n+√πn/8+O(lg n) comparisons are proven to be sufficient. n+min(k, nk)+3 ln n+O(1) comparisons are sufficient if k, the rank of x in X, differs from n/2 by Θ(n).

Keywords

Average Cost Close Neighbor Close Comparison Neighbor Problem Current Neighbor 
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.

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References

  1. 1.
    M. Blum, R.W. Floyd, V.R. Pratt, R.L. Rivest and R.E. Tarjan, Time Bounds for Selection, J. Compt. and Sys. Sci., 7, 1973, pp. 448–461.Google Scholar
  2. 2.
    W. Cunto and J.I. Munro, Closest Neighbor Problem, Proceedings 22-nd Allerton Conference, Urbana, Illinois, 1984, pp. 510–515.Google Scholar
  3. 3.
    W. Cunto and J.I. Munro, Average Case Selection, JACM, 36, 1989, pp. 270–279.Google Scholar
  4. 4.
    R.W. Floyd and R.L. Rivest, Expected Time Bounds for Selection, CACM, 18, 1975, pp. 165–172.Google Scholar
  5. 5.
    R.W. Floyd and R.L. Rivest, Algorithm 489: The Algorithm SELECT for Finding the ith Smallest of n elements, CACM, 18, 1975, pp. 173.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Walter Cunto
    • 1
  • J. Ian Munro
    • 2
  • Patricio V. Poblete
    • 3
  1. 1.Centro Científico IBM de VenezuelaCaracasVenezuela
  2. 2.Department of Computer ScienceUniversity of WaterlooWaterlooCanada
  3. 3.Departamento de Ciencias de la ComputaciónUniversidad de ChileSantiagoChile

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