Quasi-distinct Parsing and Optimal Compression Methods

  • Authors:

  • Amihood Amir;Yonatan Aumann;Avivit Levy;Yuri Roshko

  • Affiliations:

  • Department of Computer Science, Bar Ilan University, Ramat Gan, Israel 52900 and Department of Computer Science, Johns Hopkins University, Baltimore, MD 21218;Department of Computer Science, Bar Ilan University, Ramat Gan, Israel 52900;Shenkar College, Ramat Gan, Israel 52526 and CRI, Haifa University, Haifa, Israel 31905;Shenkar College, Ramat Gan, Israel 52526

  • Venue:
  • CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
  • Year:
  • 2009

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Abstract

In this paper, the optimality proof of Lempel-Ziv coding is re-studied, and a much more general compression optimality theorem is derived. In particular, the property of quasi-distinct parsing is defined. This property is much weaker than distinct parsing required in the original proof, yet we show that the theorem holds with this weaker property as well. This provides a better understanding of the optimality proof of Lempel-Ziv coding, together with a new tool for proving optimality of other compression schemes. To demonstrate the possible use of this generalization, a new coding method --- the APT coding --- is presented. This new coding method is based on a principle that is very different from Lempel-Ziv's coding. Moreover, it does not directly define any parsing technique. Nevertheless, APT coding is analyzed in this paper and using the generalized theorem shown to be asymptotically optimal up to a constant factor, if APT quasi-distinctness hypothesis holds. An empirical evidence that this hypothesis holds is also given.