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Kolmogorov Complexity, the Universal Distribution, and Worst-Case vs. Average-Case

  • Uwe Schöning
  • Randall Pruim

Abstract

An algorithm can exhibit very different complexity behavior in the worst case and in the average case (with a “uniform” distribution of inputs). One well-known example of this disparity is the QuickSort algorithm. But it is possible — by means of Kolmogorov Complexity — to define a probability distribution under which worst-case and average-case running time (for all algorithms simultaneously) are the same (up to constant factors).

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References

  1. M. Li and P. Vitanyi: An Introduction to Kolmogorov Complexity and Its Applications, 2nd edition, Springer, 1997.Google Scholar
  2. M. Li and P. Vitanyi: Average-case complexity under the universal distribution equals worst-case complexity, Information Processing Letters 42 (1992), 145–149.MathSciNetzbMATHCrossRefGoogle Scholar
  3. M. Li and P.M.B. Vitanyi: A theory of learning simple concepts and average case complexity for the universal distribution. Proceedings of the 30th Symposium on Foundations of Computer Science, IEEE, 1989.Google Scholar
  4. P.B. Milterson: The complexity of malign ensembles. SIAM Journal on Computing 22 (1993), 147–156.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Uwe Schöning
    • 1
  • Randall Pruim
    • 2
  1. 1.Abt. Theoretische InformatikUniversität UlmUlmGermany
  2. 2.Dept. of Mathematics and StatisticsCalvin CollegeGrand RapidsUSA

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