Kolmogorov Complexity, the Universal Distribution, and Worst-Case vs. Average-Case
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).
Unable to display preview. Download preview PDF.
- M. Li and P. Vitanyi: An Introduction to Kolmogorov Complexity and Its Applications, 2nd edition, Springer, 1997.Google Scholar
- 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