Abstract
We consider the problem of finding the most frequent elements in the data stream model; this problem has a linear lower bound in terms of the input length. In this paper we obtain sharper space lower bounds for this problem, not in terms of the length of the input as is traditionally done, but in terms of the quantitative properties (in this case, distribution of the element frequencies) of the input per se; this lower bound matches the best known upper bound for this problem. These bounds suggest the study of data stream algorithms through an instance-specific lens.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Muthukrishnan, S.: Data Streams: Algorithms and Applications. Now Publishers (2005)
Babcock, B., Babu, S., Datar, M., Motwani, R., Widom, J.: Models and issues in data stream systems. In: Proceedings of the 21st ACM Symposium on Principles of Databases Systems, pp. 1–16. ACM Press, New York (2002)
Alon, N., Matias, Y., Szegedy, M.: The space complexity of approximating the frequency moments. Journal of Computer and System Sciences 58(1), 137–147 (1999)
Gibbons, P., Matias, Y.: New sampling-based summary statistics for improving approximate query answers. In: Proceedings of the ACM SIGMOD International Conference on Management of Data, pp. 331–342. ACM Press, New York (1998)
Gibbons, P., Matias, Y.: Synposis data structures for massive data sets. In: Proceedings of 10th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 909–910. ACM Press, New York (1999)
Fang, M., Shivakumar, N., Garcia-Molina, H., Motwani, R., Ullman, J.: Computing iceberg queries efficiently. In: Proceedings of 22nd International Conference on Very Large Data Bases, pp. 307–317 (1996)
Charikar, M., Chen, K., Farach-Colton, M.: Finding frequent items in data streams. In: Proceedings of the 29th International Colloquium on Automata, Languages, and Programming, pp. 693–703 (2002)
Indyk, P., Woodruff, D.P.: Optimal approximations of the frequency moments of data sets. In: Proceedings of the 37th Annual ACM Symposium on Theory of Computing, pp. 202–208. ACM Press, New York (2005)
Bar-Yossef, Z., Jayram, T.S., Kumar, R., Sivakumar, D.: An information statistics approach to data stream and communication complexity. Journal of Computer and System Sciences 68(4), 702–732 (2004)
Kushilevitz, E., Nisan, N.: Communication Complexity. Cambridge University Press, Cambridge (1997)
Cover, T.M., Thomas, J.A.: Elements of Information Theory. John Wiley & Sons Inc, Chichester (1991)
Chakrabarti, A., Khot, S., Sun, X.: Near-optimal lower bounds on the multiparty communication complexity of set-disjointness. In: Proceedings of the 18th Annual IEEE Conference on Computational Complexity, pp. 107–117. IEEE Computer Society Press, Los Alamitos (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kumar, R., Panigrahy, R. (2007). On Finding Frequent Elements in a Data Stream. In: Charikar, M., Jansen, K., Reingold, O., Rolim, J.D.P. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2007 2007. Lecture Notes in Computer Science, vol 4627. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74208-1_42
Download citation
DOI: https://doi.org/10.1007/978-3-540-74208-1_42
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74207-4
Online ISBN: 978-3-540-74208-1
eBook Packages: Computer ScienceComputer Science (R0)