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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| Veröffentlicht in: | Discrete mathematics and theoretical computer science Jg. DMTCS Proceedings vol. AQ,...; H. Proceedings; S. 339 - 348 |
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DMTCS
01.01.2012
Discrete Mathematics and Theoretical Computer Science Discrete Mathematics & Theoretical Computer Science |
| Schriftenreihe: | DMTCS Proceedings |
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| ISSN: | 1365-8050, 1462-7264, 1365-8050 |
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| 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 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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| AbstractList | 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 $(2 n^{-1} \ln{n})^{1/2}$. |
| Author | Bindjeme, Patrick fill, james Allen |
| Author_xml | – sequence: 1 givenname: Patrick surname: Bindjeme fullname: Bindjeme, Patrick organization: Department of Applied Mathematics and Statistics [Baltimore] – sequence: 2 givenname: james Allen surname: fill fullname: fill, james Allen |
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| Snippet | 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... |
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| SubjectTerms | [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 |
| Title | Exact $L^2$-Distance from the Limit for QuickSort Key Comparisons (Extended Abstract) |
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