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arXiv · 1611.01479

Space-Efficient Re-Pair Compression

Philip Bille·Inge Li Gørtz·Nicola Prezza
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Abstract

Re-Pair is an effective grammar-based compression scheme achieving strong compression rates in practice. Let $n$, $\sigma$, and $d$ be the text length, alphabet size, and dictionary size of the final grammar, respectively. In their original paper, the authors show how to compute the Re-Pair grammar in expected linear time and $5n + 4\sigma^2 + 4d + \sqrt{n}$ words of working space on top of the text. In this work, we propose two algorithms improving on the space of their original solution. Our model assumes a memory word of $\lceil\log_2 n\rceil$ bits and a re-writable input text composed by $n$ such words. Our first algorithm runs in expected $\mathcal O(n/\epsilon)$ time and uses $(1+\epsilon)n +\sqrt n$ words of space on top of the text for any parameter $0<\epsilon \leq 1$ chosen in advance. Our second algorithm runs in expected $\mathcal O(n\log n)$ time and improves the space to $n +\sqrt n$ words.

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Philip Bille, Inge Li Gørtz, Nicola Prezza. 2016-11-04. Space-Efficient Re-Pair Compression. https://arxiv.org/abs/1611.01479

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