Competitive Analysis of Maintaining Frequent Items of a Stream

Abstract

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 \(\varTheta(\sqrt{N})\) and \(\varTheta(\sqrt[3]{N})\) 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.KeywordsCompetitive RatioOnline AlgorithmFrequent ItemInput StreamCompetitive AnalysisThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.