Approximate Sorting

  • Joachim Giesen
  • Eva Schuberth
  • Miloš Stojaković
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3887)


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 ν(n)+1) comparisons are always sufficient.


Sorting Ranking Spearman’s footrule metric Kendall’s tau metric 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Joachim Giesen
    • 1
  • Eva Schuberth
    • 1
    • 2
  • Miloš Stojaković
    • 1
  1. 1.Institute for Theoretical Computer ScienceETH ZürichZürichSwitzerland
  2. 2.Swiss Federal Laboratories for Materials Testing and ResearchDübendorfSwitzerland

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