Grammar-based compression in a streaming model

  • Authors:
  • Travis Gagie;Paweł Gawrychowski

  • Affiliations:
  • Department of Computer Science, University of Chile;Institute of Computer Science, University of Wrocław, Poland

  • Venue:
  • LATA'10 Proceedings of the 4th international conference on Language and Automata Theory and Applications
  • Year:
  • 2010

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Abstract

We show that, given a string s of length n, with constant memory and logarithmic passes over a constant number of streams we can build a context-free grammar that generates s and only s and whose size is within an ${\mathcal O}\left({\min \left( g \log g, \sqrt{n / \log n} \right)}\right)$-factor of the minimum g. This stands in contrast to our previous result that, with polylogarithmic memory and polylogarithmic passes over a single stream, we cannot build such a grammar whose size is within any polynomial of g.