Abstract
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.
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A preliminary version of this work was presented in part at the 26th International Colloquium on Automata, Languages, and Programming (ICALP99), Prague, Czech Republic, July 1999.
Jointly supported by the NSERC Research Grant OGP0046613 and a CITO grant, the NSERC Research Grant OGP0046506, a CITO grant, and the Steacie Fellowship, and the European Union through NeuroCOLT II ESPRIT Working Group.
JIANG Tao received the B.S. degree in computer science and technology from the University of Science and Technology of China in 1984 and the Ph.D. degree in computer science from the University of Minnesota in 1988. From Jan. 1989 to Sept. 1999, he was a faculty member at Department of Computing and Software, McMaster University, Hamilton, Ontario, Canada. During 1995–1996, he took a research leave at University of Washington, USA, and at Gunma University, Japan. He joined University of California-Riverside as a professor of computer science in Sept. 1999, while taking a leave from McMaster University.
His research interests include computational molecular biology, design and analysis of algorithms, computational complexity, and information retrieval. He has published actively in many theoretical computer science journals and served on program committees for many international conferences. He is presently serving on the editorial board of International Journal of Foundations of Computer Science (IJFCS).
LI Ming is a professor of computer science at the University of Waterloo, and a guest professor at Peking University and University of Science and Technology of China. He received his Ph.D. degree from Cornell University in 1985. He is a recipient of Canada’s prestigious E.W.R. Steacie Fellowship Award in 1996, and the 1997 Award of Merit from the Federation of Chinese Canadian Professionals. He is a coauthor of the book “An Introduction to Kolmogorov Complexity and Its Applications” (Springer-Verlag, 1993, 2nd Edition, 1997), and “A Course on Java Programming Language” (in Chinese, Science Press, 1997). He currently serves on the editorial borads of Journal of Computer and System Sciences, Journal of Computer Science and Technology, Information and Computation, and Journal of Combinatorial Optimization, International Journal of Foundation of Computer Science. His main research interests is bioinformatics. His recent book together with Paul Vitányi “Description Complexity” (Chinese, Science Press, 1999) won first prize for China’s National Science and Technology Book Award.
Paul M.B. Vitányi obtained his Ph.D. degree from the Free University of Amsterdam (the Netherlands) in 1978. He holds positions at the CWI (Center for Mathematics and Computer Science) National Research Institute in Amsterdam where he heads the Algorithms and Complexity Research Group, and at the University of Amsterdam where he heads a similar group and is a professor of computer science. He has worked in the areas of cellular automata, computational complexity, distributed and parallel computing, machine learning and prediction, physics of computation, quantum computing, and description complexity. He serves on the editorial boards of Distributed Computing, Information Processing Letters, Theory of Computing Systems, Parallel Processing Letters, and has co-authored about 150 research papers and books, among others with Li Ming “An Introduction to Kolmogorov Complexity and Its Applications”, Springer-Verlag, New York, 1993 (2nd Edition 1997), parts of which have been translated into Russian, Japanese and Chinese. (Web page: http://www.cwi.nl/$¡m$paulv/)
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Jiang, T., Li, M. & Vitányi, P.M.B. Average-case analysis of algorithms using Kolmogorov complexity. J. Comput. Sci. & Technol. 15, 402–408 (2000). https://doi.org/10.1007/BF02950402
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DOI: https://doi.org/10.1007/BF02950402