Entropy Bounds for Grammar-Based Tree Compressors
Data Structures and Algorithms
2020-05-21 v3 Information Theory
math.IT
Abstract
The definition of -order empirical entropy of strings is extended to node labelled binary trees. A suitable binary encoding of tree straight-line programs (that have been used for grammar-based tree compression before) is shown to yield binary tree encodings of size bounded by the -order empirical entropy plus some lower order terms. This generalizes recent results for grammar-based string compression to grammar-based tree compression.
Keywords
Cite
@article{arxiv.1901.03155,
title = {Entropy Bounds for Grammar-Based Tree Compressors},
author = {Danny Hucke and Markus Lohrey and Louisa Seelbach Benkner},
journal= {arXiv preprint arXiv:1901.03155},
year = {2020}
}
Comments
A short version of this paper appeared in the IEEE Proceedings of ISIT 2019