Skip to main content
Springer Nature Link
Log in

Average-case analysis via incompressibility

  • Invited Lectures
  • Conference paper
  • First Online:
Fundamentals of Computation Theory (FCT 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1279))

Included in the following conference series:

  • 108 Accesses

Abstract

We will demonstrate how to use Kolmogorov complexity to do the average-case analysis via some examples. These examples include: longest common subsequence problem and shortest common supersequence problem [9, 11], problems in computational geometry [14], average case analysis of Heapsort [19, 17], average nni-distance between two binary rooted leave-labeled trees [23], compact routing in computer networks.

Supported in part by the NSERC Operating Grant OGP0046506, ITRC, a CGAT grant, and the Steacie Fellowship.

Partially supported by the European Union through NeuroCOLT ESPRIT Working Group Nr. 8556, and by NWO through NFI Project ALADDIN under Contract number NF 62-376.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. B.E. Briley, Some new results on average worst case carry. IEEE Trans. Computers, C-22:5 (1973).

    Google Scholar 

  2. A.W. Burks, H.H. Goldstine, J. von Neumann, Preliminary discussion of the logical design of an electronic computing instrument. Institute for Advanced Studies, Report (1946). Reprinted in John von Neumann Collected Works, vol 5 (1961).

    Google Scholar 

  3. H. Buhrman, J.H. Hoepman, P.M.B. Vitányi, Optimal routing tables, Proc. 15th ACM Symp. Principles Distribut. Comput., ACM Press, 1996, 134–142.

    Google Scholar 

  4. R. Beigel, W. Gasarch, M. Li, and L. Zhang, Addition in log2 n steps on average: a simple analysis, to appear in Theoretical Computer Science (Note).

    Google Scholar 

  5. T. Cormen, C. Leiserson, and R. Rivest, Introduction to algorithms. MIT Press, 1990.

    Google Scholar 

  6. V. Chvátal and D. Sankoff, Longest common subsequences of two random sequences. J. Appl. Probab. 12 (1975), 306–315.

    Google Scholar 

  7. K. Culik JrII, D. Wood, A note on some tree similarity measures, Inform. Process. Lett., 15 (1982), 39–42.

    Article  Google Scholar 

  8. R.W. Floyd, Treesort 3: Algorithm 245, Comm. ACM, 7 (1964), 701.

    Article  Google Scholar 

  9. D. Foulser, M. Li, and Q. Yang, Theory and algorithms for plan merging. Artificial Intelligence, 57 (1992), 143–181.

    Article  Google Scholar 

  10. K. Hwang, Computer arithmetic: principles, architecture, and design. Wiley, New York, 1979.

    Google Scholar 

  11. T. Jiang and M. Li, On the approximation of shortest common supersequences and longest common subsequences. SIAM J. Comput., 24:5 (1995), 1122–1139.

    Article  Google Scholar 

  12. A.K. Jagota and K.W. Regan, Testing Neural Net Algorithms on General Compressible Data, In Proceedings of the International Conference on Neural Information Processing, Hong Kong, 1996, Springer-Verlag.

    Google Scholar 

  13. K. Kobayashi, On malign input distributions for algorithms, IEICE Trans. Inform. and Syst., E76-D:6 (1993), 634–640.

    Google Scholar 

  14. M. Li and B.H. Zhu, Applications of Kolmogorov complexity in computational geometry, manuscript, City Univ. Hong Kong, 1997.

    Google Scholar 

  15. M. Li, J. Tromp, and L. Zhang, On the nearest neighbor interchange distance, COCOON'96, Hong Kong, 1996. Final version to appear in J. Theoret. Biology, 1996.

    Google Scholar 

  16. M. Li and P. Vitányi, Average case complexity equals worst-case complexity under the Universal Distribution. Inform. Process. Lett., 42 (1992), 145–149.

    Article  MathSciNet  Google Scholar 

  17. M. Li and P. Vitányi, An introduction to Kolmogorov complexity and its applications. Springer-Verlag, New York, 1993. 2nd Edition, 1997.

    Google Scholar 

  18. P.B. Miltersen, The complexity of malign ensembles, SIAM J. Comput., 22:1 (1993), 147–156.

    Article  Google Scholar 

  19. I. Munro, Personal communication, 1993.

    Google Scholar 

  20. G. Schay, How to add fast-on average. American Mathematical Monthly, 102:8 (1995), 725–730.

    Google Scholar 

  21. R. Schaffer and R. Sedgewick, J. Algorithms, 15 (1993), 76–100.

    Article  Google Scholar 

  22. J.M. Steele, An Efron-Stein inequality for nonsymmetric statistics. Ann. Stat. 14 (1986) 753–758.

    Google Scholar 

  23. D. Sleator, R. Tarjan, and W. Thurston, Short encodings of evolving structures, SIAM J. Discr. Math., 5 (1992), 428–450.

    Article  Google Scholar 

  24. J.W.J. Williams, Algorithm 232: HEAPSORT, Comm. ACM, 7 (1964), 347–348.

    Google Scholar 

Download references

Author information

Author notes

  1. Ming Li

    Present address: Department of Computer Science, University of Waterloo, N2L 3G1, Waterloo, Canada

Authors and Affiliations

  1. Department of Computer Science, City University of Hong Kong and University of Waterloo, Kowloon, Hong Kong

    Ming Li

  2. CWI and University of Amsterdam, Kruislaan 413, 1098 SJ, Amsterdam, The Netherlands

    Paul Vitányi

Authors
  1. Ming Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Paul Vitányi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ming Li .

Editor information

Bogdan S. Chlebus Ludwik Czaja

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Li, M., Vitányi, P. (1997). Average-case analysis via incompressibility. In: Chlebus, B.S., Czaja, L. (eds) Fundamentals of Computation Theory. FCT 1997. Lecture Notes in Computer Science, vol 1279. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0036170

Download citation

  • DOI: https://doi.org/10.1007/BFb0036170

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63386-0

  • Online ISBN: 978-3-540-69529-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics