Exact $L^2$-Distance from the Limit for QuickSort Key Comparisons (Extended Abstract)

Using a recursive approach, we obtain a simple exact expression for the $L^2$-distance from the limit in the classical limit theorem of Régnier (1989) for the number of key comparisons required by $\texttt{QuickSort}$. A previous study by Fill and Janson (2002) using a similar approach found that th...

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Bibliographic Details
Published in:Discrete mathematics and theoretical computer science Vol. DMTCS Proceedings vol. AQ,...; no. Proceedings; pp. 339 - 348
Main Authors: Bindjeme, Patrick, fill, james Allen
Format: Journal Article Conference Proceeding
Language:English
Published: DMTCS 01.01.2012
Discrete Mathematics and Theoretical Computer Science
Discrete Mathematics & Theoretical Computer Science
Series:DMTCS Proceedings
Subjects:
[info.info-cg] computer science [cs]/computational geometry [cs.cg]
[info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
[info.info-ds] computer science [cs]/data structures and algorithms [cs.ds]
[math.math-co] mathematics [math]/combinatorics [math.co]
Combinatorics
Computational Geometry
Computer Science
Data Structures and Algorithms
Discrete Mathematics
key comparisons
l^2$-distance
limit distribution
Mathematics
quicksort
limit distribution
key comparisons
QuickSort
L^2$-distance
ISSN:1365-8050, 1462-7264, 1365-8050
Online Access:Get full text
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Summary:Using a recursive approach, we obtain a simple exact expression for the $L^2$-distance from the limit in the classical limit theorem of Régnier (1989) for the number of key comparisons required by $\texttt{QuickSort}$. A previous study by Fill and Janson (2002) using a similar approach found that the $d_2$-distance is of order between $n^{-1} \log{n}$ and $n^{-1/2}$, and another by Neininger and Ruschendorf (2002) found that the Zolotarev $\zeta _3$-distance is of exact order $n^{-1} \log{n}$. Our expression reveals that the $L^2$-distance is asymptotically equivalent to $(2 n^{-1} \ln{n})^{1/2}$.
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.46298/dmtcs.3003