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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| Vydané v: | Discrete mathematics and theoretical computer science Ročník DMTCS Proceedings vol. AQ,...; číslo Proceedings; s. 339 - 348 |
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| Hlavní autori: | , |
| Médium: | Journal Article Konferenčný príspevok.. |
| Jazyk: | English |
| Vydavateľské údaje: |
DMTCS
01.01.2012
Discrete Mathematics and Theoretical Computer Science Discrete Mathematics & Theoretical Computer Science |
| Edícia: | DMTCS Proceedings |
| Predmet: | |
| ISSN: | 1365-8050, 1462-7264, 1365-8050 |
| On-line prístup: | Získať plný text |
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| Shrnutí: | 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 $(2 n^{-1} \ln{n})^{1/2}$. |
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| ISSN: | 1365-8050 1462-7264 1365-8050 |
| DOI: | 10.46298/dmtcs.3003 |