Application of Lempel--Ziv factorization to the approximation of grammar-based compression

  • Authors:
  • Wojciech Rytter

  • Affiliations:
  • Instytut Informatyki, Uniwersytet Warszawski, Poland and Department of Computer Science, New Jersey Institute of Technology

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2003

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Abstract

We introduce new type of context-free grammars, AVL-grammars, and show their applicability to grammar-based compression. Using this type of grammars we present O(n log |Σ|) time and O(log n)-ratio approximation of minimal grammar-based compression of a given string of length n over an alphabet Σ and O(k log n) time transformation of LZ77 encoding of size k into a grammar-based encoding of size O(k log n). A preliminary version of this paper has been presented in Rytter (Combinatorial Pattern Matching, Lecture Notes in Computer Science, vol. 2373, Springer, Berlin, June 2000, pp. 20-31), independently of Charikar et al. (STOC, 2002), where grammar-based approximation has been attacked with different construction and a more complicated type of grammars (α-balanced grammars for α ≤ 1 - ½ √2). The AVL-grammar is a very natural and simple tool for grammar based compression, it is a straightforward extension of the classical AVL-tree.