Reductions in streaming algorithms, with an application to counting triangles in graphs

  • Authors:
  • Ziv Bar-Yossef;Ravi Kumar;D. Sivakumar

  • Affiliations:
  • University of California at Berkeley, Berkeley, CA;IBM Almaden Research Center, San Jose, CA;IBM Almaden Research Center, San Jose, CA

  • Venue:
  • SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
  • Year:
  • 2002

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Abstract

We introduce reductions in the streaming model as a tool in the design of streaming algorithms. We develop the concept of list-efficient streaming algorithms that are essential to the design of efficient streaming algorithms through reductions.Our results include a suite of list-efficient streaming algorithms for basic statistical primitives. Using the reduction paradigm along with these tools, we design streaming algorithms for approximately counting the number of triangles in a graph presented as a stream.A specific highlight of our work is the first algorithm for the number of distinct elements in a data stream that achieves arbitrary approximation factors. (Independently, Trevisan [Tre01] has solved this problem via a different approach; our algorithm has the advantage of being list-efficient.)