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arXiv · 1908.04933

Re-Pair In Small Space

Dominik Köppl·Tomohiro I·Isamu Furuya·Yoshimasa Takabatake·Kensuke Sakai·Keisuke Goto
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Abstract

Re-Pair is a grammar compression scheme with favorably good compression rates. The computation of Re-Pair comes with the cost of maintaining large frequency tables, which makes it hard to compute Re-Pair on large scale data sets. As a solution for this problem we present, given a text of length $n$ whose characters are drawn from an integer alphabet, an $O(n^2) \cap O(n^2 \lg \log_τn \lg \lg \lg n / \log_τn)$ time algorithm computing Re-Pair in $n \lg \max(n,τ)$ bits of space including the text space, where $τ$ is the number of terminals and non-terminals. The algorithm works in the restore model, supporting the recovery of the original input in the time for the Re-Pair computation with $O(\lg n)$ additional bits of working space. We give variants of our solution working in parallel or in the external memory model.

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Dominik Köppl, Tomohiro I, Isamu Furuya, Yoshimasa Takabatake, Kensuke Sakai, Keisuke Goto. 2019-11-16. Re-Pair In Small Space. https://arxiv.org/abs/1908.04933

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