A Note on Estimating Hybrid Frequency Moment of Data Streams

  • Authors:

  • Sumit Ganguly

  • Affiliations:

  • Indian Institute of Technology, Kanpur,

  • Venue:
  • AAIM '09 Proceedings of the 5th International Conference on Algorithmic Aspects in Information and Management
  • Year:
  • 2009

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Abstract

We consider the problem of estimating the hybrid frequency moment of matrix data that is updated point-wise in arbitrary order by a data stream. In this model, data is viewed to be organized in the form of a matrix (A i ,j )1 ≤ i ,j , ≤ n . The entries A i ,j are updated coordinate-wise (both increments and decrements are allowed), in arbitrary order and possibly multiple times. The hybrid frequency moment F p ,q (A ) is defined as $\sum_{j=1}^n\left( \sum_{i=1}^n \lvert{A_{i,j}}\rvert^p\right)^q$ and is a generalization of the frequency moment of one-dimensional data streams. Prior work [10] presented a nearly space-optimal algorithm for estimating F p ,q for p *** [0,2] and q *** [0,1]. Here, we complement that work by presenting a nearly space-optimal algorithm for estimating F p ,q for p *** [0,1] and q *** [0,2].