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Algorithms 2012, 5(2), 214-235; doi:10.3390/a5020214

Article

An Online Algorithm for Lightweight Grammar-Based Compression

Shirou Maruyama ¹ , Hiroshi Sakamoto ²  and Masayuki Takeda ^1,*

¹ Department of Informatics, Kyushu University, 744 Motooka Nishi-ku Fukuoka-shi, Fukuoka, Japan ² Graduate School of Computer Science and Systems Engineering, Kyushu Institute of Technology,680-4 Kawazu Iizuka-shi Fukuoka, Japan

* Author to whom correspondence should be addressed.

Received: 30 January 2012; in revised form: 26 March 2012 / Accepted: 28 March 2012 / Published: 10 April 2012

(This article belongs to the Special Issue Data Compression, Communication and Processing)

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Abstract: Grammar-based compression is a well-studied technique to construct a context-free grammar (CFG) deriving a given text uniquely. In this work, we propose an online algorithm for grammar-based compression. Our algorithm guarantees O(log² n)- approximation ratio for the minimum grammar size, where n is an input size, and it runs in input linear time and output linear space. In addition, we propose a practical encoding, which transforms a restricted CFG into a more compact representation. Experimental results by comparison with standard compressors demonstrate that our algorithm is especially effective for highly repetitive text.

Keywords: lossless compression; grammar-based compression; online algorithm; approximation algorithm

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