Competitive analysis of maintaining frequent items of a stream

We study the well-known frequent items problem in data streams 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 and 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. © 2012 Springer-Verlag