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1 UIC - Department of Mathematics, Statistics and Computer Science Chicago 2 Department of Computer Science Purdue

Abstract : We consider the standard Quicksort algorithm that sorts n distinct keys with all possible n! orderings of keys being equally likely. Equivalently, we analyze the total path length Ln in a randomly built \emphbinary search tree. Obtaining the limiting distribution of Ln is still an outstanding open problem. In this paper, we establish an integral equation for the probability density of the number of comparisons Ln. Then, we investigate the large deviations of Ln. We shall show that the left tail of the limiting distribution is much -thinner- i.e., double exponential than the right tail which is only exponential. Our results contain some constants that must be determined numerically. We use formal asymptotic methods of applied mathematics such as the WKB method and matched asymptotics.

Keywords : Algorithms Analysis of algorithms Asymptotic analysis Binary search tree Quicksort Sorting

Autor: Charles Knessl - Wojciech Szpankowski -

Fuente: https://hal.archives-ouvertes.fr/


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