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Approximate Sorting

Giesen J., Schuberth E., Stojaković M.

Fundamenta Informaticae

2009

Vol. 90, nr 1-2

67-72

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 (n) comparisons are always sufficient. Keywords: algorithms, sorting, ranking, Spearman's footrule metric, Kendall's tau metri