Abstract
We present deterministic sub-linear space algorithms for problems over update data streams, including, estimating frequencies of items and ranges, finding approximate frequent items and approximate φ-quantiles, estimating inner-products, constructing near-optimal B-bucket histograms and estimating entropy. We also present improved lower bound results for several problems over update data streams.
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References
Alon, N., Gibbons, P.B., Matias, Y., Szegedy, M.: Tracking Join and Self-Join Sizes in Limited Storage. In: Proc. ACM PODS, ACM Press, New York (1999)
Babcock, B., Babu, S., Datar, M., Motwani, R., Widom, J.: Models and Issues in Data Stream Systems. In: Proc. ACM PODS, ACM Press, New York (2002)
Bhuvanagiri, L., Ganguly, S.: Estimating Entropy over Data Streams. In: Azar, Y., Erlebach, T. (eds.) ESA 2006. LNCS, vol. 4168, pp. 148–159. Springer, Heidelberg (2006)
Bose, P., Kranakis, E., Morin, P., Tang, Y.: Bounds for Frequency Estimation of Packet Streams. In: SIROCCO, pp. 33–42 (2003)
Chakrabarti, A., Cormode, G., McGregor, A.: A Near-Optimal Algorithm for Computing the Entropy of a Stream. In: Proc. ACM SODA, ACM Press, New York (2007)
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)
Cormode, G., Garofalakis, M.: Sketching Streams Through the Net: Distributed Approximate Query Tracking. In: Proc. VLDB (September 2005)
Cormode, G., Korn, F., Muthukrishnan, S., Srivastava, D.: Finding Hierarchical Heavy Hitters in Data Streams. In: Proc. VLDB (2003)
Cormode, G., Muthukrishnan, S.: What’s New: Finding Significant Differences in Network Data Streams. In: IEEE INFOCOM, IEEE Computer Society Press, Los Alamitos (2004)
Cormode, G., Muthukrishnan, S.: An Improved Data Stream Summary: The Count-Min Sketch and its Applications. J. Algorithms 55(1), 58–75 (2005)
Cormode, G., Muthukrishnan, S.: What’s hot and what’s not: tracking most frequent items dynamically. ACM Trans. Database Syst. 30(1), 249–278 (2005)
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, Springer, Heidelberg (2002)
Estan, C., Savage, S., Varghese, G.: Automatically inferring patterns of resource consumption in network traffic. In: Proc. ACM SIGCOMM, pp. 137–148. ACM Press, New York (2003)
Ganguly, S., Kesh, D., Saha, C.: Practical Algorithms for Tracking Database Join Sizes. In: Ramanujam, R., Sen, S. (eds.) FSTTCS 2005. LNCS, vol. 3821, Springer, Heidelberg (2005)
Ganguly, S., Majumder, A.: Deterministic K-set Structure. In: Proc. ACM PODS, ACM Press, New York (2006)
Gibbons, P.B., Matias, Y.: New Sampling-Based Summary Statistics for Improving Approximate Query Answers. In: Proc. ACM SIGMOD, ACM Press, New York (1998)
Gilbert, A., Guha, S., Indyk, P., Kotidis, Y., Muthukrishnan, S., Strauss, M.: Fast Small-space Algorithms for Approximate Histogram Maintenance. In: Proc. ACM STOC, ACM Press, New York (2002)
Gilbert, A., Kotidis, Y., Muthukrishnan, S., Strauss, M.: How to Summarize the Universe: Dynamic Maintenance of Quantiles. In: Bressan, S., Chaudhri, A.B., Lee, M.L., Yu, J.X., Lacroix, Z. (eds.) CAiSE 2002 and VLDB 2002. LNCS, vol. 2590, Springer, Heidelberg (2003)
Gilbert, A.C., Kotidis, Y., Muthukrishnan, S., Strauss, M.J.: Surfing Wavelets on Streams: One-pass Summaries for Approximate Aggregate Queries. In: Jonker, W. (ed.) VLDB-WS 2001 and DBTel 2001. LNCS, vol. 2209, Springer, Heidelberg (2001)
Greenwald, M., Khanna, S.: Space-efficient online computation of quantile summaries. In: SIGMOD (2001)
Hershberger, J., Shrivastava, N., Suri, S., Toth, C.D.: Space Complexity of Hierarchical Heavy Hitters in Multi-Dimensional Data Streams. In: Proc. ACM PODS, ACM Press, New York (2005)
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)
Manku, G., Motwani, R.: Approximate Frequency Counts over Data Streams. In: Bressan, S., Chaudhri, A.B., Lee, M.L., Yu, J.X., Lacroix, Z. (eds.) CAiSE 2002 and VLDB 2002. LNCS, vol. 2590, pp. 346–357. Springer, Heidelberg (2003)
Manku, G., Rajagopalan, S., Lindsay, B.: Random sampling techniques for space efficient online computation of order statistics of large datasets. In: Proc. ACM SIGMOD, ACM Press, New York (1999)
Misra, J., Gries, D.: Finding repeated elements. Sci. Comput. Programm. 2, 143–152 (1982)
Muthukrishnan, S.: Data Streams: Algorithms and Applications. Foundations and Trends in Theoretical Computer Science 1(2) (2005)
Rosser, J.B.: Explicit bounds on some functions on prime numbers. Amer. J. Math. 63 (1941)
Schweller, R., Li, Z., Chen, Y., Gao, Y., Gupta, A., Zhang, Y., Dinda, P., Kao, M-Y., Memik, G.: Monitoring Flow-level High-speed Data Streams with Reversible Sketches. In: IEEE INFOCOM, IEEE Computer Society Press, Los Alamitos (2006)
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Ganguly, S., Majumder, A. (2007). CR-precis: A Deterministic Summary Structure for Update Data Streams. In: Chen, B., Paterson, M., Zhang, G. (eds) Combinatorics, Algorithms, Probabilistic and Experimental Methodologies. ESCAPE 2007. Lecture Notes in Computer Science, vol 4614. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74450-4_5
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DOI: https://doi.org/10.1007/978-3-540-74450-4_5
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