On Finding Frequent Elements in a Data Stream

Authors:
Ravi Kumar;Rina Panigrahy
Affiliations:
Yahoo! Research, 701 First Ave, Sunnyvale, CA 94089, USA;Microsoft Research, 1065 La Avenida, Mountain View, CA 94043, USA
Venue:
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Year:
2007

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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.