## Electronic Journal of Probability

### The number of bit comparisons used by Quicksort: an average-case analysis

#### Abstract

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.

#### Article information

Source
Electron. J. Probab., Volume 17 (2012), paper no. 43, 22 pp.

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

https://projecteuclid.org/euclid.ejp/1465062365

Digital Object Identifier
doi:10.1214/EJP.v17-1812

Mathematical Reviews number (MathSciNet)
MR2928726

Zentralblatt MATH identifier
1244.68090

Subjects
Primary: 60C05: Combinatorial probability

Rights

#### Citation

Fill, James; Janson, Svante. The number of bit comparisons used by Quicksort: an average-case analysis. Electron. J. Probab. 17 (2012), paper no. 43, 22 pp. doi:10.1214/EJP.v17-1812. https://projecteuclid.org/euclid.ejp/1465062365

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