Competitive analysis of maintaining frequent items of a stream

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 Θ(N) and Θ(N3) 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≥1k≥1