Competitive Analysis of Maintaining Frequent Items of a Stream

a r t i c l e i n f o a b s t r a c t 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(3 √ 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