Quicksort asymptotics

Journal of Algorithms

Volumn 44, Issue 1, 2002, Pages 4-28

  Fill, James Allen ^a   Janson, Svante ^b  

^a JOHNS HOPKINS UNIVERSITY   (United States)

^b UPPSALA UNIVERSITY   (Sweden)

Author keywords

Asymptotics; Coupling; dp metric; Density; Kolmogorov Smirnov distance; Limit distribution; Moment generating function; Numerical analysis; Quicksort; Rate of convergence; Sorting algorithm

Indexed keywords

ASYMPTOTIC STABILITY; CONVERGENCE OF NUMERICAL METHODS; MATHEMATICAL TRANSFORMATIONS; SORTING;

MOMENT GENERATING FUNCTIONS;

ALGORITHMS;

EID: 0036660145     PISSN: 01966774     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0196-6774(02)00216-X     Document Type: Article

References (17)

1. S. Cambanis, G. Simons, W. Stout, Inequalities for E k(X, Y) when the marginals are fixed, Z. Wahrscheinlichkeit. Geb. 36 (1976) 285-294.
2. L. Devroye, J.A. Fill, R. Neininger, Perfect simulation from the Quicksort limit distribution, Electron. Comm. Probab. 5 (2000) 95-99 (electronic).
3. J. Dongarra, F. Sullivan, Guest editors' introduction: the top 10 algorithms, Comput. Sci. Engrg. 2 (1) (2000) 22-23.
4. J.A. Fill, On the distribution for binary search trees under the random permutation model, Random Structures Algorithms 8 (1996) 1-25.
5. J.A. Fill, S. Janson, Smoothness and decay properties of the limiting Quicksort density function, in: D. Gardy, A. Mokkadem (Eds.), Mathematics and Computer Science: Algorithms, Trees, Combinatorics and Probabilities, in: Trends Math., Birkhäuser, 2000, pp. 53-64.
6. J.A. Fill, S. Janson, A characterization of the set of fixed points of the Quicksort transformation, Electron. Comm. Probab. 5 (2000) 77-84 (electronic).
7. J.A. Fill, S. Janson, Approximating the limiting Quicksort distribution, Random Structures Algorithms 19 (2001) 376-406.
8. J.A. Fill, S. Janson, Appendix to Quicksort asymptotics. Unpublished appendix to this paper, available from http://www.mts.jhu.edu/̃fill/ or http://www.math.uu.se/~svante/.
9. P. Hennequin, Analyse en moyenne d'algorithmes, tri rapide et arbres de recherche. PhD dissertation, École Polytechnique Palaiseau.
10. C. Knessl, W. Szpankowski, Quicksort algorithm again revisited, Discrete Math. Theor. Comput. Sci. 3 (1999) 43-64.
11. D.E. Knuth, Fundamental Algorithms, The Art of Computer Programming, Vol. 1, 3rd edition, Addison-Wesley, Reading, MA, 1997.
12. D.E. Knuth, Sorting and Searching, The Art of Computer Programming, Vol. 3, 2nd edition, Addison-Wesley, Reading, MA, 1998.
13. C.J.H. McDiarmid, R.B. Hayward, Large deviations for Quicksort, J. Algorithms 21 (1996) 476-507.
14. R. Neininger, L. Rüschendorf, Rates of convergence for Quicksort, J. Algorithms, to appear.
15. M. Régnier, A limiting distribution for quicksort, RAIRO Inform. Théor. Appl. 23 (1989) 335-343.
16. U. Rösler, A limit theorem for 'Quicksort', RAIRO Inform. Théor. Appl. 25 (1991) 85-100.
17. K.H. Tan, P. Hadjicostas, Some properties of a limiting distribution in Quicksort, Statist. Probab. Lett. 25 (1995) 87-94.