Grammar-Based Compression in a Streaming Model

TL;DR

This paper demonstrates that with limited memory and multiple passes over multiple streams, it is possible to efficiently generate a near-optimal context-free grammar for a string, improving upon previous limitations.

Contribution

It introduces a streaming model for grammar-based compression that achieves near-optimal grammar size with constant memory and logarithmic passes over multiple streams.

Findings

Achieves grammar size within an { ext{min}(g \, ext{log} g, \, ext{sqrt}(n \, ext{log} g))} of the optimal

Contrasts with previous results showing limitations with polylogarithmic memory and single stream

Shows feasibility of efficient grammar-based compression in streaming models

Abstract

We show that, given a string $s$ of length $n$, with constant memory and logarithmic passes over a constant number of streams we can build a context-free grammar that generates $s$ and only $s$ and whose size is within an $\Oh{\min (g \log g, \sqrt{n \log g})}$-factor of the minimum $g$. This stands in contrast to our previous result that, with polylogarithmic memory and polylogarithmic passes over a single stream, we cannot build such a grammar whose size is within any polynomial of $g$.