Open Access
Translator Disclaimer
2012 The number of bit comparisons used by Quicksort: an average-case analysis
James Fill, Svante Janson
Author Affiliations +
Electron. J. Probab. 17: 1-22 (2012). DOI: 10.1214/EJP.v17-1812


The analyses of many algorithms and data structures (such as digital search trees) for searching and sorting are based on the representation of the keys involved as bit strings and so count the number of bit comparisons. On the other hand, the standard analyses of many other algorithms (such as Quicksort) are performed in terms of the number of key comparisons. We introduce the prospect of a fair comparison between algorithms of the two types by providing an average-case analysis of the number of bit comparisons required by Quicksort. Counting bit comparisons rather than key comparisons introduces an extra logarithmic factor to the asymptotic average total. We also provide a new algorithm, "BitsQuick", that reduces this factor to constant order by eliminating needless bit comparisons.


Download Citation

James Fill. Svante Janson. "The number of bit comparisons used by Quicksort: an average-case analysis." Electron. J. Probab. 17 1 - 22, 2012.


Accepted: 6 June 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1244.68090
MathSciNet: MR2928726
Digital Object Identifier: 10.1214/EJP.v17-1812

Primary: 60C05
Secondary: 68W40

Keywords: average-case analysis of algorithms , poissonization , QuickSort


Vol.17 • 2012
Back to Top