Re-Pair In Small Space

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 $O(n^2)\cap O(n^2\lg {\log }_{\tau }n\lg \lg \lg n/{\log }_{\tau }n)$ time algorithm computing Re-Pair in $n\lg \max (n,\tau )$ bits of space including the text space, where $\tau$ 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.