Grammar-based Compression of Unranked Trees

TL;DR

This paper introduces forest straight-line programs (FSLPs) for efficiently compressing unranked ordered trees, compares their succinctness with existing methods, and provides polynomial-time algorithms for tree equality testing under certain algebraic conditions.

Contribution

It presents FSLPs as a novel compression scheme for unranked trees, along with translation methods and polynomial-time equality testing algorithms for specific algebraic properties.

Findings

FSLPs generalize tree straight-line programs and are comparable in succinctness.

Efficient translation algorithms between FSLPs, top dags, and first-child/next sibling encodings.

Polynomial-time tree equality testing when symbols are associative or commutative.

Abstract

We introduce forest straight-line programs (FSLPs) as a compressed representation of unranked ordered node-labelled trees. FSLPs are based on the operations of forest algebra and generalize tree straight-line programs. We compare the succinctness of FSLPs with two other compression schemes for unranked trees: top dags and tree straight-line programs of first-child/next sibling encodings. Efficient translations between these formalisms are provided. Finally, we show that equality of unranked trees in the setting where certain symbols are associative or commutative can be tested in polynomial time. This generalizes previous results for testing isomorphism of compressed unordered ranked trees.