On the analysis of stochastic divide and conquer algorithms

Algorithmica (New York)

Volumn 29, Issue 1-2, 2001, Pages 238-261

  Rosler U ^a  

^a UNIVERSITY OF KIEL   (Germany)

Author keywords

Asymptotics; Average analysis; Cauchy problem; Dirichlet problem; Divide and conquer algorithm; Invariant function; Recursive equation; Renewal equation; Renewal process

Indexed keywords

MARKOV PROCESSES; PROBLEM SOLVING; RANDOM PROCESSES; RECURSIVE FUNCTIONS; THEOREM PROVING;

RENEWAL EQUATIONS;

ALGORITHMS;

EID: 9644259154     PISSN: 01784617     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02679621     Document Type: Article

References (25)

1. Alsmeyer, G. Erneuerungstheorie. Teubner, 1991.
2. Bertram-Kretzberg, C. Analyse von Quicksort-Varianten. Diplomarbeit, Dortmund, 1991.
3. Bickel, P.J., and Freedman, D.A. Some asymptotic theory for the bootstrap. Annals of Probability 9, 1196-1217, 1981.
4. Bruhn, V. Eine Methode zur asymptotischen Behandlung einer Klasse von Rekursionsgleichungen mit einer Anwendung in der stochastischen Analyse des Quicksort-Algorithmus. Dissertation, Christian-Albrechts-Universität zu Kiel, 1996.
5. Dobrow, R.P., and Fill, J.A. Total path length for random recursive trees. Preprint to appear in Combinatorics, Probability & Computing.
6. van Emden, M.H. Increasing the efficiency of Quicksort. Communications of the Association for Computing Machinery 13, 563-567, 1970.
7. Flajolet, P. Analytic Analysis of Algorithms. Lecture Notes in Computer Science, vol. 623, pp. 186-210, Ed. W. Kuich, Springer-Verlag, Berlin, 1992.
8. Grübel, R., and Rösler, U. Asymptotic distribution theory for Hoare's selection algorithm. Advances in Applied Probability 28, 252-269, 1996.
9. Hennequin, P. Combinatorial analysis of Quicksort algorithm. Informatique théorique et Applications/ Theoretical Informatics and Applications 23, 317-333, 1989.
10. Hoare, C.A.R. Algorithm 64: Quicksort. Communications of the Association for Computing Machinery 4, 321, 1961.
11. Hoare, C.A.R. Quicksort. Computer Journal 5, 10-15, 1962.
12. Knuth, D.E. The Art of Computer Programming, Vol. 3. Addison-Wesley, Reading, MA, 1973.
13. McDiarmid, C., and Hayward, R. Strong concentration for Quicksort. Proceedings of the Third Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 414-421, 1992.
14. Paulsen, V. The moment of FIND. Journal of Applied Probability 34, 1079-1082, 1997.
15. Rachev, S.T., and Rüschendorf, L. Probability metrics and recursive algorithms. Advances in Applied Probability 27, 770-799, 1995.
16. Rösler, U. A limit theorem for "Quicksort. Informatique théorique et Applications/Theoretical Informatics and Applications 15, 85-100, 1991.
17. Rösler, U. A fixed point theorem for distributions. Stochastic Processes and their Applications 42, 195-214, 1992.
18. Rösler, U. The view backwards on the Algorithms FIND. Berichtsreihe des Mathematischen Seminars Kiel, Christian-Albrechts-Universität zu Kiel, www.numerik.uni-kiel/reports/ Bericht 99-?, 1998.
19. Rösler, U. Orlicz norms for measures. Berichtsreihe des Mathematischen Seminars Kiel, Christian-Albrechts-Universität zu Kiel, www.numerik.uni-kiel/reports/ Bericht 99-?, 1998.
20. Rösler, U., and Rüschendorf, L. The contraction method for recursive algorithms. Algorithmica, this issue.
21. Roura, S. An improved Master Theorem for divide-and-conquer recurrences. Proceedings of the 24th International Colloquium (ICALP-97), pp. 449-459, 1997.
22. Sedgewick, R. The analysis of Quicksort programs. Acta Informatica 7, 327-355, 1977.
23. Sedgewick, R. Quicksort. Stanford Computer Science Report STAN-CS-75-492, Ph.D. thesis; 1975. Also published by Garland, New York, 1980.
24. Sedgewick, R. Algorithms, Second edition. Addison-Wesley, Reading, MA, 1988.
25. Sedgewick, R., and Flajolet, P. An Introduction to the Analysis of Algorithms. Addison-Wesley, Reading, MA, 1996.