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...
Gespeichert in:
| Veröffentlicht in: | Discrete mathematics and theoretical computer science Jg. DMTCS Proceedings vol. AQ,...; H. Proceedings; S. 339 - 348 |
|---|---|
| Hauptverfasser: | , |
| Format: | Journal Article Tagungsbericht |
| Sprache: | Englisch |
| Veröffentlicht: |
DMTCS
01.01.2012
Discrete Mathematics and Theoretical Computer Science Discrete Mathematics & Theoretical Computer Science |
| Schriftenreihe: | DMTCS Proceedings |
| Schlagworte: | |
| ISSN: | 1365-8050, 1462-7264, 1365-8050 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Zusammenfassung: | 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 |