Re²Pair: Increasing the Scalability of RePair by Decreasing Memory Usage

The RePair compression algorithm produces a context-free grammar by iteratively substituting the most frequently occurring pair of consecutive symbols with a new symbol until all consecutive pairs of symbols appear only once in the compressed text. It is widely used in the settings of bioinformatics, machine learning, and information retrieval where random access to the original input text is needed. For example, in pangenomics, RePair is used for random access to a population of genomes. BigRePair improves the scalability of the original RePair algorithm by using Prefix-Free Parsing (PFP) to preprocess the text prior to building the RePair grammar. Despite the efficiency of PFP on repetitive text, there is a scalability issue with the size of the parse which causes a memory bottleneck in BigRePair. In this paper, we design and implement recursive RePair (denoted as $$ ), which builds the RePair grammar using recursive PFP. Our novel algorithm faces the challenge of constructing the RePair grammar without direct access to the parse of text, relying solely on the dictionary of the text and the parse and dictionary of the parse of the text. We compare $$ to BigRePair using SARS-CoV-2 haplotypes and haplotypes from the 1000 Genomes Project. We show that our method $$ achieves over a 40% peak memory reduction and a speed up ranging between 12% to 79% compared to BigRePair when compressing the largest input texts in all experiments. $$ is made publicly available under the GNU public license here: https://github.com/jkim210/Recursive-RePair.