arXiv subjects

Isamu Furuya

Publications and source records attributed to Isamu Furuya.

4 recordsLinked to original sources

arXiv2019

Re-Pair In Small Space

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.

cs.DS↗

arXiv2019

Practical Repetition-Aware Grammar Compression

The goal of grammar compression is to construct a small sized context free grammar which uniquely generates the input text data. Among grammar compression methods, RePair is known for its good practical compression performance. MR-RePair was recently proposed as an improvement to RePair for constructing small-sized context free grammar for repetitive text data. However, a compact encoding scheme has not been discussed for MR-RePair. We propose a practical encoding method for MR-RePair and show its effectiveness through comparative experiments. Moreover, we extend MR-RePair to run-length context free grammar and design a novel variant for it called RL-MR-RePair. We experimentally demonstrate that a compression scheme consisting of RL-MR-RePair and the proposed encoding method show good performance on real repetitive datasets.

cs.DS↗

arXiv2019

MR-RePair: Grammar Compression based on Maximal Repeats

We analyze the grammar generation algorithm of the RePair compression algorithm and show the relation between a grammar generated by RePair and maximal repeats. We reveal that RePair replaces step by step the most frequent pairs within the corresponding most frequent maximal repeats. Then, we design a novel variant of RePair, called MR-RePair, which substitutes the most frequent maximal repeats at once instead of substituting the most frequent pairs consecutively. We implemented MR-RePair and compared the size of the grammar generated by MR-RePair to that by RePair on several text corpus. Our experiments show that MR-RePair generates more compact grammars than RePair does, especially for highly repetitive texts.

cs.DS↗

arXiv2017

Compaction of Church Numerals for Higher-Order Compression

In this study, we address the problem of compacting Church numerals. Church numerals appear as a representation of the repetitive part of data in higher-order compression. We propose a novel decomposition scheme for a natural number using tetration, which leads to a compact representation of $λ$-terms equivalent to the original Church numerals. For natural number $n$, we prove that the size of the $λ$-term obtained by the proposed method is $O(({\rm slog}_{2}n)^{\log n/ \log \log n})$. Moreover, we quantitatively confirmed experimentally that the proposed method outperforms a binary expression of Church numerals when $n$ is less than approximately 10000.

cs.DS↗