Distributional convergence for the number of symbol comparisons used by QuickSort

d Abstract) James Allen Fill1† 1 Department of Applied Mathematics and Statistics, The Johns Hopkins University, 34th and Charles Streets, Baltimore, MD 21218-2682 USA received 28 Feb 2010, revised 30th May 2010, accepted tomorrow. Most previous studies of the sorting algorithm QuickSort have used the number of key comparisons as a measure of the cost of executing the algorithm. Here we suppose that the n independent and identically distributed (iid) keys are each represented as a sequence of symbols from a probabilistic source and that QuickSort operates on individual symbols, and we measure the execution cost as the number of symbol comparisons. Assuming only a mild “tameness” condition on the source, we show that there is a limiting distribution for the number of symbol comparisons after normalization: first centering by the mean and then dividing by n. Additionally, under a condition that grows more restrictive as p increases, we have convergence of moments of orders p and s...

• Type: Journal
• Year: 2012
• Where: CORR
• Authors: James Allen Fill
• Keywords: Charles Streets, CORR 2012, Education, Johns Hopkins University, Sorting Algorithm