The frequent items problem, under polynomial decay, in the streaming model

Guy Feigenblat, Ofra Itzhaki, Ely Porat

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We consider the problem of estimating the frequency count of data stream elements under polynomial decay functions. In these settings every element in the stream is assigned with a time-decreasing weight, using a non-increasing polynomial function. Decay functions are used in applications where older data is less significant, less interesting or even less reliable than recent data. Consider a data stream of N elements drawn from a universe U. We propose three poly-logarithmic algorithms for the problem. The first one, deterministic, uses O(1/2logN(loglogN+logU)) bits, where ∈(0,1) is the approximation parameter. The second one, probabilistic, uses O(12logNδlog1) bits or O(12logNδlogN) bits, depending on the decay function parameter, where δ∈(0,1) is the probability of failure. The third one, deterministic in the stochastic model, uses O(1logU) bits or O(12logN) bits, also depending on the decay parameter as will be described in this paper. This variant of the problem is important and has many applications. To our knowledge, it has never been studied before.

Original languageEnglish
Pages (from-to)3048-3054
Number of pages7
JournalTheoretical Computer Science
Issue number34-36
StatePublished - 17 Jul 2010


  • Algorithms
  • Frequency count
  • Polynomial decay functions
  • Streaming


Dive into the research topics of 'The frequent items problem, under polynomial decay, in the streaming model'. Together they form a unique fingerprint.

Cite this