Introduction

Data compression is one of those areas where small insights can lead to big improvements. Over the years, we've seen a variety of successful approaches, from dictionary-based methods like LZ77 and LZW to grammar-based techniques like Sequitur. While these approaches have their strengths, I've been exploring a slightly different idea—a hierarchical tree-based compression method that borrows from existing techniques but introduces a structured parent-child relationship to organize the data.

The Core Idea

The basic concept is to create a tree-based dictionary structure where each node (or dictionary entry) can have multiple children but only one parent. This setup allows you to efficiently compress complex, structured data by breaking it down into smaller building blocks and referencing them hierarchically.

How It Works:

Identify Small Patterns: Start by breaking the data into small binary chunks.
Build a Dictionary: Identify repeated chunks and promote them to dictionary entries.
Hierarchical Structure: New dictionary entries can reference existing entries, creating a multi-level tree.
Recursive Compression: As patterns emerge at higher levels, the dictionary can grow deeper, capturing complex structures more efficiently.
Encoding: Replace repeated patterns with compact index references, using variable-length encoding to maximize efficiency.

This approach allows for efficient reuse of components at different levels, making it well-suited for compressing structured data with recurring motifs.

Why a Tree Structure?

Most dictionary-based compression methods rely on flat or loosely connected dictionaries. By introducing a structured tree, you gain a few key advantages:

Efficient Organization: A tree ensures that the data has a clear, predictable decoding path.
Simpler Decoding: Since each node has only one parent, decoding is straightforward—just follow the tree down from the root.
Pattern Hierarchies: Many types of data (e.g., multimedia files, structured text, or serialized objects) naturally form hierarchical patterns, which a tree-based dictionary can capture more effectively than a flat structure.

How It Differs from Grammar-Based Compression

At first glance, this might sound similar to grammar-based compression methods like Sequitur, which also build hierarchical patterns by replacing repeated substrings. However, there are some key differences:

Explicit Dictionary Management: Grammar-based methods work by building implicit rules. In contrast, this approach manages a concrete dictionary where entries are explicitly defined and indexed.
Single Parent Constraint: Each dictionary entry has only one parent in the tree, which simplifies encoding and decoding. Grammar-based approaches allow more flexible referencing, which can complicate decoding.
Controlled Complexity: The tree structure gives more control over how the dictionary is built and managed, potentially improving compression ratios while keeping decoding fast.

Encoding and Hybrid Compression

To further improve compression, the tree-based structure can be combined with standard entropy encoding techniques:

Index Encoding: Use Huffman or arithmetic coding to encode the dictionary indices.
Residual Data: For data that doesn’t fit into the dictionary structure, apply secondary compression (e.g., run-length encoding or direct entropy coding) to handle the remaining bits efficiently.
Adaptive Strategy: Tune the sliding window size, promotion thresholds, and encoding settings based on the characteristics of the input data.

Why This Approach Could Work

The hierarchical tree structure allows you to represent complex patterns with fewer references, which means better compression for structured data. This approach should excel with data that exhibits repeated patterns at multiple levels—like nested objects, multimedia streams, and structured file formats.

The tree ensures that decoding remains straightforward, even as the dictionary grows. Unlike DAG-based approaches (where a single chunk can have multiple parents), the single-parent constraint prevents conflicts and simplifies the decoding path.

Conclusion

This hierarchical tree-based compression method blends elements from dictionary and grammar-based compression while introducing a structured parent-child tree model. It offers the potential for higher compression ratios, especially for structured and patterned data.

By focusing on smart chunk promotion, efficient tree organization, and hybrid entropy coding, this method could become a tool for handling complex data more efficiently. The goal is to create a solution that excels in compression scenarios where other approaches struggle.

Hierarchical Tree-Based Compression