Approximate sorting

Authors:
Joachim Giesen;Eva Schuberth;Miloš Stojaković
Affiliations:
Institute for Theoretical Computer Science, ETH Zürich, Zürich;Institute for Theoretical Computer Science, ETH Zürich, Zürich;Institute for Theoretical Computer Science, ETH Zürich, Zürich
Venue:
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Year:
2006

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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 n2/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.