Kurt Sieber | Searcharxiv

arXiv2018

Grammar-based Compression of Unranked Trees

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.

cs.DS↗

arXiv2017

Optimal top dag compression

It is shown that for a given ordered node-labelled tree of size $n$ and with $s$ many different node labels, one can construct in linear time a top dag of height $O(\log n)$ and size $O(n / \log_σn) \cap O(d \cdot \log n)$, where $σ= \max\{ 2, s\}$ and $d$ is the size of the minimal dag. The size bound $O(n / \log_σn)$ is optimal and improves on previous bounds.

cs.DS↗