On the expected lengths of sequences generated in sorting by replacement selecting

  • Authors:

  • William W. Hooker

  • Affiliations:

  • Lockheed Missiles and Space Company, Palo Alto, CA

  • Venue:
  • Communications of the ACM
  • Year:
  • 1969

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Abstract

In the replacement-selecting technique of sorting, one is interested in the ratio Lj of the expected length of the jth sequence generated by the technique to the number of memory cells used. Using complex-variable theory, it is shown that Lj → 2 and that, asymtotically, the average interval between sign changes of Lj — 2 is 2.6662.