Abstract
In this paper we investigate variants of the well-known Hoare’s Quickfind algorithm for the selection of the j-th element out of n when recursion stops for subfiles whose size is below a predefined threshold and a simpler algorithm is run instead. We provide estimates for the combined number of passes, comparisons and exchanges under three policies for the small subfiles: insertion sort and two variants of selection sort, but the analysis could be easily adapted for alternative policies. We obtain the average cost for each of these variants and compare them with the costs of the standard variant which does not use cutoff. We also give the best explicit cutoff bound for each of the variants.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Anderson, D., and Brown, R. Combinatorial aspects of C.A.R. Hoare’s FIND algorithm. Australasian Journal of Combinatorics 5 (1992), 109–119.
Hoare, C. Find (Algorithm 65). Communications of the ACM. (1961), 321–322.
Hoare, C. Quicksort. Computer Journal 5 (1962), 10–15.
HWANG, H.-K., AND TSAI, T.-H. Quickselect and Dickman function. Combinatorics, Probability and Computing (2002). To appear.
Kirschenhofer, P., Prodinger, H., And Martínez, C. Analysis of Hoare’s FIND algorithm with median-of-three partition. Random Structures 14 Algorithms 10 (1997), 143–156.
Knuth, D. Mathematical analysis of algorithms. In Information Processing ‘71, Proc. of the 1971 IFIP Congress (Amsterdam, 1972), North-Holland, pp. 19–27.
Knuth, D. The Art of Computer Programming: Sorting and Searching, 2nd ed., vol. 3. Addison-Wesley, Reading, Mass., 1998.
Martínez, C., and Roura, S. Optimal sampling strategies in Quicksort and quickselect. SIAM Journal on Computing 31, 3 (2001), 683–705.
Sedgewick, R. The analysis of Quicksort programs. Acta Informatica 7 (1976), 327–355.
Sedgewick, R. Implementing Quicksort programs Communications of the ACM 21 (1978), 847–856.
Sedgewick, R. Quicksort. Garland, New York, 1978.
Sedgewick, R., and Flajolet, P. An Introduction to the Analysis of Algorithms. Addison-Wesley, Reading, Mass., 1996.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Basel AG
About this paper
Cite this paper
Martínez, C., Panario, D., Viola, A. (2002). Analysis of Quickfind with Small Subfiles. In: Chauvin, B., Flajolet, P., Gardy, D., Mokkadem, A. (eds) Mathematics and Computer Science II. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8211-8_20
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8211-8_20
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9475-3
Online ISBN: 978-3-0348-8211-8
eBook Packages: Springer Book Archive