Space-Efficient Re-Pair Compression

TL;DR

This paper introduces two space-efficient algorithms for Re-Pair grammar compression, significantly reducing working space while maintaining expected linear or near-linear time performance.

Contribution

The authors propose two novel algorithms that improve space efficiency of Re-Pair compression, with one achieving near-linear time and minimal extra space.

Findings

First algorithm runs in expected O(n/ε) time with (1+ε)n + √n space.

Second algorithm runs in expected O(n log n) time with n + √n space.

Both algorithms outperform previous solutions in space while maintaining efficiency.

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.