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http://dx.doi.org/10.18419/opus-13112
Autor(en): | Stober, Florian Weiß, Armin |
Titel: | On the average case of MergeInsertion |
Erscheinungsdatum: | 2020 |
Dokumentart: | Zeitschriftenartikel |
Seiten: | 1197-1224 |
Erschienen in: | Theory of computing systems 64 (2020), S. 1197-1224 |
URI: | http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-ds-131314 http://elib.uni-stuttgart.de/handle/11682/13131 http://dx.doi.org/10.18419/opus-13112 |
ISSN: | 1432-4350 1433-0490 |
Zusammenfassung: | MergeInsertion, also known as the Ford-Johnson algorithm, is a sorting algorithm which, up to today, for many input sizes achieves the best known upper bound on the number of comparisons. Indeed, it gets extremely close to the information-theoretic lower bound. While the worst-case behavior is well understood, only little is known about the average case. This work takes a closer look at the average case behavior. In particular, we establish an upper bound of nlogn-1.4005n+o(n) comparisons. We also give an exact description of the probability distribution of the length of the chain a given element is inserted into and use it to approximate the average number of comparisons numerically. Moreover, we compute the exact average number of comparisons for n up to 148. Furthermore, we experimentally explore the impact of different decision trees for binary insertion. To conclude, we conduct experiments showing that a slightly different insertion order leads to a better average case and we compare the algorithm to Manacher’s combination of merging and MergeInsertion as well as to the recent combined algorithm with (1,2)-Insertionsort by Iwama and Teruyama. |
Enthalten in den Sammlungen: | 05 Fakultät Informatik, Elektrotechnik und Informationstechnik |
Dateien zu dieser Ressource:
Datei | Beschreibung | Größe | Format | |
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s00224-020-09987-4.pdf | 1,95 MB | Adobe PDF | Öffnen/Anzeigen |
Diese Ressource wurde unter folgender Copyright-Bestimmung veröffentlicht: Lizenz von Creative Commons