# Online Grammar Compression for Frequent Pattern Discovery

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Shouhei Fukunaga,
Yoshimasa Takabatake,
Tomohiro I,
Hiroshi Sakamoto
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Proceedings of The 13th International Conference on Grammatical Inference, PMLR 57:93-104, 2017.

#### Abstract

Various grammar compression algorithms have been proposed in the last decade. A grammar compression is a restricted CFG deriving the string deterministically. An efficient grammar compression develops a smaller CFG by finding duplicated patterns and removing them. This process is just a frequent pattern discovery by grammatical inference. While we can get any frequent pattern in linear time using a preprocessed string, a huge working space is required for longer patterns, and the whole string must be loaded into the memory preliminarily. We propose an online algorithm approximating this problem within a compressed space. The main contribution is an improvement of the previously best known approximation ratio Ω(\frac1\lg^2m) to Ω(\frac1\lg^*N\lg m) where m is the length of an optimal pattern in a string of length N and \lg^* is the iteration of the logarithm base 2. For a sufficiently large N, \lg^*N is practically constant. The experimental results show that our algorithm extracts nearly optimal patterns and achieves a significant improvement in memory consumption compared to the offline algorithm.

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