We study the classic frequent items problem in data streams, but from a competitive analysis point of view. We consider the standard worst-case input model, as well as a weaker distributional adversarial setting. We are primarily interested in the single-slot memory case and for both models we give (asymptotically) tight bounds of Theta(root N) and Theta(3 root N) respectively, achieved by very simple and natural algorithms, where N is the stream's length. We also provide lower bounds, for both models, in the more general case of arbitrary memory sizes of k >= 1 (C) 2014 Elsevier B.V. All rights reserved.
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