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Adaptive Spatial Partitioning for Multidimensional Data Streams

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3341))

Abstract

We propose a space-efficient scheme for summarizing multidimensional data streams. Our scheme can be used for several geometric queries, including natural spatial generalizations of well-studied single-dimensional queries such as icebergs and quantiles.

Research by the last three authors was partially supported by National Science Foundation grants CCR-0049093 and IIS-0121562.

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References

  1. Agarwal, P.K., Har-Peled, S., Varadarajan, K.R.: Approximating extent measures of points. J. ACM 51, 606–635 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  2. Alon, N., Matias, Y., Szegedy, M.: The space complexity of approximating the frequency moments. J. Comput. Syst. Sci. 58, 137–147 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  3. Arasu, A., Manku, G.: Approximate counts and quantiles over sliding windows. In: Proc. 23rd PODS, pp. 286–296. ACM Press, New York (2004)

    Google Scholar 

  4. Babcock, B., Babu, S., Datar, M., Motwani, R., Widom, J.: Models and issues in data stream systems. In: 21st PODS, pp. 1–16. ACM Press, New York (2002)

    Google Scholar 

  5. Bentley, J.L.: Multidimensional divide-and-conquer. Communications of the ACM 23(4), 214–229 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  6. Charikar, M., O’Callaghan, L., Panigrahy, R.: Better streaming algorithms for clustering problems. In: Proc. 35th STOC, pp. 30–39 (2003)

    Google Scholar 

  7. Cormode, G., Korn, F., Muthukrishnan, S., Srivastava, D.: Finding hierarchical heavy hitters in data streams. In: Proc. 29th Conf. VLDB (2003)

    Google Scholar 

  8. Cormode, G., Muthukrishnan, S.: Radial histograms for spatial streams. Technical report DIMACS TR 2003-11 (2003)

    Google Scholar 

  9. Cormode, G., Muthukrishnan, S.: What is hot and what is not: Tracking most frequent items dynamically. In: Proc. 22nd PODS, pp. 296–306 (2003)

    Google Scholar 

  10. Datar, M., Gionis, A., Indyk, P., Motwani, R.: Maintaining stream statistics over sliding windows. SIAM Journal of Computing 31(6), 1794–1813 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  11. 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 

  12. Estan, C., Savage, S., Varghese, G.: Automatically inferring patterns of resource consumption in network traffic. In: Proc. SIGCOMM, pp. 137–148. ACM Press, New York (2003)

    Google Scholar 

  13. Fang, M., Shivakumar, N., Garcia-Molina, H., Motwani, R., Ullman, J.D.: Computing iceberg queries efficiently. In: Proc. 24rd Conf. VLDB, pp. 299–310 (1998)

    Google Scholar 

  14. Gilbert, A., Kotidis, Y., Muthukrishnan, S., Strauss, M.: How to summarize the Universe: Dynamic maintenance of quantiles. In: Proc. 28th Conf. on VLDB (2002)

    Google Scholar 

  15. Greenwald, M., Khanna, S.: Space-efficient online computation of quantile summaries. In: Proc. 20th SIGMOD, pp. 58–66 (2001)

    Google Scholar 

  16. Hershberger, J., Suri, S.: Adaptive sampling for geometric problems over data streams. In: Proc. 23rd PODS, pp. 252–262. ACM Press, New York (2004)

    Google Scholar 

  17. Karp, R.M., Shenker, S., Papadimitriou, C.H.: A simple algorithm for finding frequent elements in streams and bags. ACM Transactions on Database Systems 28(1), 51–55 (2003)

    Article  Google Scholar 

  18. Manku, G., Motwani, R.: Approximate frequency counts over data streams. In: Proc. 28th Conf. VLDB, pp. 346–357 (2002)

    Google Scholar 

  19. Manku, G.S., Rajagopalan, S., Lindsay, B.G.: Approximate medians and other quantiles in one pass and with limited memory. In: Proc. 17th SIGMOD, pp. 426–435 (1998)

    Google Scholar 

  20. Manku, G., Rajagopalan, S., Lindsay, B.G.: Random sampling techniques for space efficient online computation of order statistics of large datasets. In: Proc. 18th SIGMOD, pp. 251–262 (1999)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  22. Munro, J.I., Paterson, M.S.: Selection and sorting with limited storage. Theoretical Computer Science 12, 315–323 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  23. Muthukrishnan, S.: Data streams: Algorithms and applications. Preprint (2003)

    Google Scholar 

  24. Suri, S., Tóth, C.D., Zhou, Y.: Range counting over multi-dimensional data streams. In: Proc. 20th ACM Symp. Comput. Geom., pp. 160–169. ACM Press, New York (2004)

    Google Scholar 

  25. Thaper, N., Guha, S., Indyk, P., Koudas, N.: Dynamic multidimensional histograms. In: Proc. SIGMOD Conf. on Management of Data, pp. 428–439. ACM Press, New York (2002)

    Google Scholar 

  26. Vapnik, V.N., Chervonenkis, A.Y.: On the uniform convergence of relative frequencies of events to their probabilities. Theory Probab. Appl. 16, 264–280 (1971)

    Article  MATH  Google Scholar 

  27. Vitter, J.S.: Random sampling with a reservoir. ACM Trans. Math. Software 11, 37–57 (1985)

    Article  MATH  MathSciNet  Google Scholar 

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© 2004 Springer-Verlag Berlin Heidelberg

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Hershberger, J., Shrivastava, N., Suri, S., Tóth, C.D. (2004). Adaptive Spatial Partitioning for Multidimensional Data Streams. In: Fleischer, R., Trippen, G. (eds) Algorithms and Computation. ISAAC 2004. Lecture Notes in Computer Science, vol 3341. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30551-4_46

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  • DOI: https://doi.org/10.1007/978-3-540-30551-4_46

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24131-7

  • Online ISBN: 978-3-540-30551-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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