Rates of convergence for Quicksort

The normalized number of key comparisons needed to sort a list of randomly permuted items by the Quicksort algorithm is known to converge in distribution. We identify the rate of convergence to be of the order (ln(n)/n) in the Zolotarev metric. This implies several ln(n)/n estimates for other distances and local approximation results as for characteristic functions, for density approximation, and for the integrated distance of the distribution functions. AMS subject classifications. Primary: 60F05, 68Q25; secondary: 68P10. Key words. Quicksort, analysis of algorithms, rate of convergence, Zolotarev metric, local approximation, contraction method.

• Type: Journal
• Year: 2002
• Where: JAL
• Authors: Ralph Neininger, Ludger Rüschendorf
• Keywords: JAL 2002, Local Approximation, Normalized Number, Quicksort Algorithm