Space-Efficient Re-Pair Compression

Re-Pair [5] is an effective grammar-based compression scheme achieving strong compression rates in practice. Let n, σ, 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 + 4σ2 + 4d + √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 [log2n] bits and a re-writable input text composed by n such words. Our first algorithm runs in expected O(n/ϵ) time and uses (1 + ϵ)n + √n words of space on top of the text for any parameter 0