Approximate sorting

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.