Competitive Analysis of Maintaining Frequent Items of a Stream

  • Yiannis Giannakopoulos
  • Elias Koutsoupias
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7357)


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.


Competitive Ratio Online Algorithm Frequent Item Input Stream Competitive Analysis 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Yiannis Giannakopoulos
    • 1
  • Elias Koutsoupias
    • 1
  1. 1.Department of InformaticsUniversity of AthensGreece

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