Approximate Sorting

  • Authors:
  • Joachim Giesen;Eva Schuberth;Miloš Stojaković

  • Affiliations:
  • Max Plank Institute for Computer Science, Saarbrücken, Germany. jgiesen@mpi-inf.mpg.de;Institute for Theoretical Computer Science, ETH Zurich, Switzerland. eva.schuberth@inf.ethz.ch;(Correspd.) Department of Mathematics and Informatics, University of Novi Sad, Serbia. smilos@inf.ethz.ch

  • Venue:
  • Fundamenta Informaticae
  • Year:
  • 2009

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Abstract

We show that any comparison based, randomized algorithm to approximate any given ranking of n items within expected Spearman's footrule distance n$^{2}$/ν(n) needs at least n (min{log ν(n), log n} − 6) comparisons in the worst case. This bound is tight up to a constant factor since there exists a deterministic algorithm that shows that 6n log (n) comparisons are always sufficient.