Tree compression using string grammars

TL;DR

This paper investigates representing ranked trees with string grammars (SLPs), showing they are more succinct than tree grammars but still support efficient computation of certain tree properties, while some problems remain intractable.

Contribution

It demonstrates that SLPs can exponentially compress trees compared to TSLPs and identifies which tree queries remain efficient or become intractable.

Findings

SLPs are exponentially more succinct than TSLPs for tree representation.

Certain queries like height and navigation are efficiently computable on SLPs.

Pattern matching and automata evaluation are intractable on SLPs.

Abstract

We study the compressed representation of a ranked tree by a (string) straight-line program (SLP) for its preorder traversal, and compare it with the well-studied representation by straight-line context free tree grammars (which are also known as tree straight-line programs or TSLPs). Although SLPs turn out to be exponentially more succinct than TSLPs, we show that many simple tree queries can still be performed efficiently on SLPs, such as computing the height and Horton-Strahler number of a tree, tree navigation, or evaluation of Boolean expressions. Other problems on tree traversals turn out to be intractable, e.g. pattern matching and evaluation of tree automata.