Approximating the limiting Quicksort distribution

Approximating the limiting Quicksort distribution

The limiting distribution of the normalized number of comparisons used by Quicksort to sort an array of n numbers is known to be the unique fixed point with zero mean of a certain distributional transformation S. We study the convergence to the limiting distribution of the sequence of distributions obtained by iterating the transformation S, beginning with a (nearly) arbitrary starting distribu...

On the tails of the limiting Quicksort distribution

We give asymptotics for the left and right tails of the limiting Quicksort distribution. The results agree with, but are less precise than, earlier non-rigorous results by Knessl and Spankowski.

The limiting distribution for the number of symbol comparisons used by QuickSort is nondegenerate (extended abstract)

In a continuous-time setting, Fill (2012) proved, for a large class of probabilistic sources, that the number of symbol comparisons used by QuickSort, when centered by subtracting the mean and scaled by dividing by time, has a limiting distribution, but proved little about that limiting random variable Y —not even that it is nondegenerate. We establish the nondegeneracy of Y . The proof is perh...

The Limiting Distribution for the Number of Symbol Comparisons Used by Quicksort Is Nondegenerate

In a continuous-time setting, Fill [2] proved, for a large class of probabilistic sources, that the number of symbol comparisons used by QuickSort, when centered by subtracting the mean and scaled by dividing by time, has a limiting distribution, but proved little about that limiting random variable Y —not even that it is nondegenerate. We establish the nondegeneracy of Y . The proof is perhaps...

Approximating the Limiting Qui ksort