# Universal Tree Source Coding Using Grammar-Based Compression

## TL;DR

This paper introduces a universal tree source coding method using grammar-based compression, improving worst-case redundancy bounds and enabling efficient lossless compression of structured binary trees.

## Contribution

It presents a novel application of tree straight-line programs for universal lossless compression, with improved redundancy bounds over previous methods.

## Key findings

- Derived tighter upper bounds on maximal pointwise redundancy.
- Developed universal codes for new classes of structured tree sources.
- Enhanced compression efficiency for binary tree data.

## Abstract

We apply so-called tree straight-line programs to the problem of lossless compression of binary trees. We derive upper bound on the maximal pointwise redundancy (or worst-case redundancy) that improve previous bounds obtained by Zhang, Yang, and Kieffer using directed acyclic graphs. Using this, we obtain universal codes for new classes of structered tree sources.