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

Document Type

Article

Publication Date

6-13-2003

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(nlog|Σ|) time and O(logn)-ratio approximation of minimal grammar-based compression of a given string of length n over an alphabet Σ and O(klogn) time transformation of LZ77 encoding of size k into a grammar-based encoding of size O(klogn). 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. © 2002 Elsevier Science B.V. All rights reserved.

Identifier

0038238644 (Scopus)

Publication Title

Theoretical Computer Science

External Full Text Location

https://doi.org/10.1016/S0304-3975(02)00777-6

ISSN

03043975

First Page

211

Last Page

222

Issue

1-3

Volume

302

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