Skip to main content

Urn Models and Yao’s Formula

  • Conference paper
  • First Online:
Database Theory — ICDT’99 (ICDT 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1540))

Included in the following conference series:

  • 2472 Accesses

Abstract

Yao’s formula is one of the basic tools in any situation where one wants to estimate the number of blocks to be read in answer to some query. We show that such situations can be modelized by probabilistic urn models. This allows us to fully characterize the distribution probability of the number of selected blocks under uniformity assumptions, and to consider extensions to non-uniform block probabilities. We also obtain a computationnally effcient approximation of Yao’s formula.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. A. Bender and L.B. Richmond Multivariate asymptotique for product of large powers with applications to Lagrange inversion. Technical report, University of Waterloo, April 1998.

    Google Scholar 

  2. A.F. Cardenas Analysis and performance of inverted data base structures. Comm. ACM, 19(5), 1975.

    Google Scholar 

  3. S. Christodoulakis Issues in query evaluation Database Engineering, 5(3) 220–223 September 1982.

    Google Scholar 

  4. S. Christodoulakis Estimating block selectivities Information Systems, 9(1) 69–79 1983.

    Article  Google Scholar 

  5. P. Flajolet and R. Sedgewick. An introduction to the analysis of algorithms. Addison-Wesley, 1996.

    Google Scholar 

  6. G. Gardarin, J.-R. Gruser, and Z.H. Tang. A cost model for clustered object oriented databases. In 21st VLDB Conference, Zürich, Switzerland, pages 323–334, 1995.

    Google Scholar 

  7. D. Gardy. Normal limiting distributions for projection and semijoin sizes. SIAM Journal on Discrete Mathematics, 5(2):219–248, May 1992.

    Article  MATH  MathSciNet  Google Scholar 

  8. D. Gardy and L. Nemirovski. Formule de Yao et modeles d’urnes. In 14st BDA Conference, Hammamet, Tunisia, (to appear) 1998.

    Google Scholar 

  9. D. Gardy and L. Nemirovski. Une application des modèles d’urnes aux bases de données: la formule de Yao et ses extensions. Technical report, Laboratoire PRISM, Université de Versailles, October 1998.

    Google Scholar 

  10. N.L. Johnson and S. Kotz. Urn models and their application. Wiley & Sons, 1977.

    Google Scholar 

  11. V. KOLCHIN, B. SEVAST'YANOV, and V. CHISTYAKOV Random Allocations. Wiley & Sons, 1978.

    Google Scholar 

  12. S.B. Yao. Approximating block accesses in data base organizations. Comm. ACM, 20(4), 1977.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gardy, D., Némirovski, L. (1999). Urn Models and Yao’s Formula. In: Beeri, C., Buneman, P. (eds) Database Theory — ICDT’99. ICDT 1999. Lecture Notes in Computer Science, vol 1540. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49257-7_8

Download citation

  • DOI: https://doi.org/10.1007/3-540-49257-7_8

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65452-0

  • Online ISBN: 978-3-540-49257-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics