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Data Stream Algorithms via Expander Graphs

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Algorithms and Computation (ISAAC 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5369))

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Abstract

We present a simple way of designing deterministic algorithms for problems in the data stream model via lossless expander graphs. We illustrate this by considering two problems, namely, k-sparsity testing and estimating frequency of items.

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References

  1. Alon, N.: Perturbed identity matrices have high rank: proof and applications (2006), http://www.math.tau.ac.il/~nogaa/identity.pdf

  2. Bose, P., Kranakis, E., Morin, P., Tang, Y.: Bounds for Frequency Estimation of Packet Streams. In: Proc. of SIROCCO, pp. 33–42 (2003)

    Google Scholar 

  3. Candès, E., Romberg, J., Tao, T.: Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inf. Theory 52(2), 489–509 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  4. Capalbo, M., Reingold, O., Vadhan, S., Wigderson, A.: Randomness conductors and constant degree lossless expanders. In: Proc. of ACM STOC (2002)

    Google Scholar 

  5. Charikar, M., Chen, K., Farach-Colton, M.: Finding frequent items in data streams. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, pp. 693–703. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  6. Cheblus, B., Kowalski, D.R.: Almost Optimal Explicit Selectors. In: Liśkiewicz, M., Reischuk, R. (eds.) FCT 2005. LNCS, vol. 3623, pp. 270–280. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  7. Cormode, G., Muthukrishnan, S.: An Improved Data Stream Summary: The Count-Min Sketch and its Applications. J. Algo. 55(1)

    Google Scholar 

  8. De Bonis, A., Gàsieniec, L., Vaccaro, U.: Generalized framework for selectors with applications in optimal group testing. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 81–96. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  9. Demaine, E.D., López-Ortiz, A., Munro, J.I.: Frequency estimation of internet packet streams with limited space. In: Möhring, R.H., Raman, R. (eds.) ESA 2002. LNCS, vol. 2461, pp. 348–360. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  10. Donoho, D.: Compressed sensing. IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  11. Eppstein, D., Goodrich, M.T.: Space-Efficient Straggler Identification in Round-Trip Data Streams. In: Dehne, F., Sack, J.-R., Zeh, N. (eds.) WADS 2007. LNCS, vol. 4619, pp. 637–648. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  12. Ganguly, S.: Counting distinct items over update streams. In: Deng, X., Du, D.-Z. (eds.) ISAAC 2005. LNCS, vol. 3827, pp. 505–514. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  13. Ganguly, S.: Lower bounds for frequency estimation over data streams. In: Hirsch, E.A., Razborov, A.A., Semenov, A., Slissenko, A. (eds.) Computer Science – Theory and Applications. LNCS, vol. 5010, pp. 204–215. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  14. Ganguly, S., Majumder, A.: CR-precis: A Deterministic Summary Structure for Update Streams. In: Chen, B., Paterson, M., Zhang, G. (eds.) ESCAPE 2007. LNCS, vol. 4614, pp. 48–59. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  15. Ganguly, S., Majumder, A.: Deterministic K-set Structure. In: Proc. ACM PODS, pp. 280–289 (2006)

    Google Scholar 

  16. Ganguly, S., Majumder, A.: Deterministic K-set Structure. Manuscript under review (July 2006), http://www.cse.iitk.ac.in/users/sganguly

  17. Gilbert, A., Guha, S., Indyk, P., Kotidis, Y., Muthukrishnan, S., Strauss, M.: Fast Small-space Algorithms for Approximate Histogram Maintenance. In: Proc. ACM STOC, pp. 152–161 (2002)

    Google Scholar 

  18. Gilbert, A., Strauss, M., Tropp, J., Vershynin, R.: One sketch for all: Fast algorithms for Compressed Sensing. In: Proc. ACM STOC (2007)

    Google Scholar 

  19. Hoory, S., Linial, N., Wigderson, A.: Expander graphs and their applications. Draft of book (2006)

    Google Scholar 

  20. Indyk, P.: Explicit Constructions for Compressed Sensing of Sparse Signals. In: Proc. ACM SODA (2008)

    Google Scholar 

  21. Karp, R.M., Shenker, S., Papadimitriou, C.H.: A Simple Algorithm for Finding Frequent Elements in Streams and Bags. ACM TODS 28(1), 51–55 (2003)

    Article  Google Scholar 

  22. Minsky, Y., Trachtenberg, A., Zippel, R.: Set Reconciliation with Nearly Optimal Communication Complexity. IEEE Trans. Inf. Theory 49(9), 2213–2218

    Google Scholar 

  23. Misra, J., Gries, D.: Finding repeated elements. Sci. Comput. Programm. 2, 143–152 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  24. Schmidt, J., Siegel, A., Srinivasan, A.: Chernoff-Hoeffding Bounds with Applications for Limited Independence. In: Proc. ACM SODA, pp. 331–340 (1992)

    Google Scholar 

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Author information

Authors and Affiliations

  1. IIT Kanpur, India

    Sumit Ganguly

Authors
  1. Sumit Ganguly
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Editor information

Editors and Affiliations

  1. School of Information Technologies, University of Sydney, Australia

    Seok-Hee Hong

  2. Graduate School of Informatics, Kyoto University, 606-8501, Kyoto, Japan

    Hiroshi Nagamochi

  3. Graduate School of Informatics, Kyoto University, Japan

    Takuro Fukunaga

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© 2008 Springer-Verlag Berlin Heidelberg

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Ganguly, S. (2008). Data Stream Algorithms via Expander Graphs. In: Hong, SH., Nagamochi, H., Fukunaga, T. (eds) Algorithms and Computation. ISAAC 2008. Lecture Notes in Computer Science, vol 5369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92182-0_8

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  • DOI: https://doi.org/10.1007/978-3-540-92182-0_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-92181-3

  • Online ISBN: 978-3-540-92182-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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