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 ν(n)+1) comparisons are always sufficient.
Partly supported by the Swiss National Science Foundation under the grant “Robust Algorithms for Conjoint Analysis” and by the joint Berlin/Zurich graduate program Combinatorics, Geometry and Computation, financed by ETH Zurich and the German Science Foundation (DFG).
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Giesen, J., Schuberth, E., Stojaković, M. (2006). Approximate Sorting. In: Correa, J.R., Hevia, A., Kiwi, M. (eds) LATIN 2006: Theoretical Informatics. LATIN 2006. Lecture Notes in Computer Science, vol 3887. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11682462_49
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DOI: https://doi.org/10.1007/11682462_49
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