Journal of Computer Science and Technology

, Volume 15, Issue 5, pp 402–408 | Cite as

Average-case analysis of algorithms using Kolmogorov complexity

  • Jiang Tao Email author
  • Li Ming 
  • Paul M. B. Vitányi


Analyzing the average-case complexity of algorithms is a very practical but very difficult problem in computer science. In the past few years, we have demonstrated that Kolmogorov complexity is an important tool for analyzing the average-case complexity of algorithms. We have developed the incompressibility method. In this paper, several simple examples are used to further demonstrate the power and simplicity of such method. We prove bounds on the average-case number of stacks (queues) required for sorting sequential or parallel Queuesort or Stacksort.


Kolmogorov complexity algorithm average-case analysis sorting 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Knuth D. E. The Art of Computer Programming. Vol.3: Sorting and Searching, Addison-Wesley, 1973 (1st Edition), 1998 (2nd Edition).Google Scholar
  2. [2]
    Tarjan R E. Sorting using networks of queues and stacks.Journal of the ACM, 1972, 19: 341–346.zbMATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    Jiang T, Li M, Vitányi P. A lower bound on the average-case complexity of Shellsort.J. Assoc. Comp. Mach., to appear. Also inICALP’99, July 11–15, 1999, Prague.Google Scholar
  4. [4]
    Li M, Vitányi P M B. An Introduction to Kolmogorov Complexity and Its Applications. Springer-Verlag, New York, 2nd Edition, 1997.zbMATHGoogle Scholar
  5. [5]
    Buhrman H, Jiang T, Li M, Vitányi P. New applications of the incompressibility method. InICALP’99, July 11–15, 1999, Prague. Also inTheoretical Computer Science, 1999, 235.Google Scholar
  6. [6]
    Kolmogorov A N. Three approaches to the quantitative definition of information.Problems Inform. Transmission, 1965, 1(1): 1–7.MathSciNetGoogle Scholar
  7. [7]
    Kerov S V, Versik A M. Asymptotics of the Plancherel measure on symmetric group and the limiting form of the Young tableaux.Soviet Math. Dokl., 1977, 18: 527–531.zbMATHGoogle Scholar
  8. [8]
    Kingman J F C. The ergodic theory of subadditive stochastic processes.Ann. Probab., 1973, 1: 883–909.zbMATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    Logan B F, Shepp L A. A variational problem for random Young tableaux.Advances in Math., 1977, 26: 206–222.zbMATHCrossRefMathSciNetGoogle Scholar
  10. [10]
    Shell D L. A high-speed sorting procedure.Commun. ACM, 1959, 2(7): 30–32.CrossRefGoogle Scholar

Copyright information

© Science Press, Beijing China and Allerton Press Inc. 2000

Authors and Affiliations

  1. 1.Department of Computing ScienceUniversity of CaliforniaRiversideUSA
  2. 2.Department of Computer ScienceUniversity of CaliforniaSanta BarbaraUSA
  3. 3.CWI and University of AmsterdamAmsterdamThe Netherlands

Personalised recommendations