Deterministic Splitter Finding in a Stream with Constant Storage and Guarantees

  • Tobias Lenz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4288)


In this paper the well-known problem of finding the median of an ordered set is studied under a very restrictive streaming model with sequential read-only access to the data. Only a constant number of reference objects from the stream can be stored for comparison with subsequent stream elements. A first non-trivial bound of \(\Omega(\sqrt{n})\) distance to the extrema of the set is presented for a single pass over streams which do not reveal their total size n. For cases with known size, an algorithm is given which guarantees a distance of Ω(n 1 − ε) to the extrema, which is an ε-approximation for the proven best bound possible.


Sensor Node Single Pass Good Splitter Constant Memory Stream Element 
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  1. 1.
    Blum, M., Floyd, R.W., Pratt, V.R., Rivest, R.L., Tarjan, R.E.: Time bounds for selection. J. Comput. Syst. Sci. 7(4), 448–461 (1973)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Greenwald, M., Khanna, S.: Space-efficient online computation of quantile summaries. In: SIGMOD 2001: Proceedings of the 2001 ACM SIGMOD international conference on Management of data, pp. 58–66. ACM Press, New York (2001)CrossRefGoogle Scholar
  3. 3.
    Guha, S., McGregor, A.: Approximating quantiles and the order of the stream. In: PODS (2006)Google Scholar
  4. 4.
    Guha, S., McGregor, A., Venkatasubramanian, S.: Streaming and sublinear approximation of entropy and information distances. In: SODA (2006)Google Scholar
  5. 5.
    Jain, R., Chlamtac, I.: The p2 algorithm for dynamic calculation of quantiles and histograms without storing observations. Commun. ACM 28(10), 1076–1085 (1985)CrossRefGoogle Scholar
  6. 6.
    Manku, G.S., Rajagopalan, S., Lindsay, B.G.: Approximate medians and other quantiles in one pass and with limited memory. SIGMOD Rec. 27(2), 426–435 (1998)CrossRefGoogle Scholar
  7. 7.
    Munro, J.I., Paterson, M.: Selection and sorting with limited storage. Theoretical Computer Science 12, 315–323 (1980)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Munro, J.I., Raman, V.: Selection from read-only memory and sorting with minimum data movement. Theoretical Computer Science 165(2), 311–323 (1996)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Paterson, M.: Progress in selection. In: Karlsson, R., Lingas, A. (eds.) SWAT 1996. LNCS, vol. 1097, pp. 368–379. Springer, Heidelberg (1996)Google Scholar
  10. 10.
    Vitter, J.S.: Random sampling with a reservoir. ACM Trans. Math. Softw. 11(1), 37–57 (1985)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Tobias Lenz
    • 1
  1. 1.Freie Universität BerlinBerlinGermany

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