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− 1 2 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.
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