Efficiently Storing a Huffman Tree for Data Compression

When it comes to Huffman coding, storing the constructed Huffman tree for efficient decoding is a key consideration. This article delves into techniques for compressing the tree representation for compact output. Below is a detailed analysis of a proposed solution:

Proposed Approach

Instead of storing the actual frequencies, the method focuses on encoding the structure of the tree:

• For Leaf Nodes: Output a 1-bit followed by the N-bit character value.
• For Non-Leaf Nodes: Output a 0-bit, then encode both child nodes recursively.

Decoding Process:

• Read a bit:

  • 1: Read N-bit character and create a new leaf node.
  • 0: Recursively decode left and right child nodes and create a new non-leaf node.

Analysis:

Calculating Output Size:

• Tree Size = 10 * Number of Characters - 1 (leaves and non-leaves)
• Encoded Size = Sum (Frequency * Path Length for each character)

Benefits:

• The bit-wise encoding enables precise output size calculation before writing.
• The tree structure is preserved without frequency information, which is redundant for decoding.

Example:

Consider the input text: AAAAAABCCCCCCDDEEEEE

• Tree:

    20

  ----------
  | 8
  | -------

  12	3

  A C E B D

• 6 5 1 2

• Paths:

  • A: 00
  • B: 110
  • C: 01
  • D: 111
  • E: 10

• Calculation:

  • Tree Size = 59 bits = 8 bytes
  • Encoded Size = 43 bits = 6 bytes
• Output: 7 bytes (tree encoded data), compared to 20 bytes for storing the original characters.

Conclusion

This approach provides an efficient and compact representation of Huffman trees for data compression applications. By encoding the tree structure directly, it saves space while preserving the information necessary for decoding. The method enables the estimation of output size in advance and can complement both whole-file and chunked data compression scenarios.