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Average-Case Analysis Using Kolmogorov Complexity

In: Advances in Algorithms, Languages, and Complexity

Author

Listed:
  • Ming Li

    (City University of Hong Kong
    University of Waterloo
    University of Waterloo, Department of Computer Science)

  • Paul Vitányi

    (CWI and University of Amsterdam)

Abstract

This expository paper demonstrates how to use Kolmogorov complexity to do the average-case analysis via four examples, and exhibits a surprising property of the celebrated associated universal distribution. The four examples are: average case analysis of Heapsort [17, 15], average nni-distance between two binary rooted leave-labeled trees [20], compact routing in computer networks [3], average-case analysis of an adder algorithm [4]. The property is that the average-case complexity of any algorithm whatsoever equals its worst-case complexity if the inputs are distributed according to the Universal Distribution [14]. We provide the proofs for the latter three items.

Suggested Citation

  • Ming Li & Paul Vitányi, 1997. "Average-Case Analysis Using Kolmogorov Complexity," Springer Books, in: Ding-Zhu Du & Ker-I Ko (ed.), Advances in Algorithms, Languages, and Complexity, pages 157-169, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-3394-4_7
    DOI: 10.1007/978-1-4613-3394-4_7
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