Discrete Mathematics & Theoretical Computer Science |

252

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

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 L(n) in a randomly built \emphbinary search tree. Obtaining the limiting distribution of L(n) is still an outstanding open problem. In this paper, we establish an integral equation for the probability density of the number of comparisons L(n). Then, we investigate the large deviations of L(n). 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.

Source: HAL:hal-00958926v1

Volume: Vol. 3 no. 2

Published on: January 1, 1999

Imported on: March 26, 2015

Keywords: Algorithms,Analysis of algorithms,Asymptotic analysis,Binary search tree,Quicksort,Sorting,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

Funding:

- Source : OpenAIRE Graph
*Towards Analytic Information Theory: Data Compression, Prediction and Universal Coding Through Analytic Methods*; Funder: National Science Foundation; Code: 9804760*Data Compression from the String Matching Perspective: Second Order Properties*; Funder: National Science Foundation; Code: 9415491

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