How Can Huffman Tree Storage be Optimized for Chunked Encoding?

Efficient Huffman Tree Storage

When implementing Huffman encoding and decoding, efficiently storing the constructed Huffman tree is crucial, especially when encoding large files in chunks.

Challenges:

In the case of reading the entire file at once, tree storage is less of a concern, but for chunked encoding, where the tree is output with each chunk, space optimization becomes essential.

Proposed Solution:

Encode the tree using a bit-wise approach:

• Leaf nodes: 1-bit N-bit character/byte.
• Non-leaf nodes: 0-bit Encoded left child Encoded right child.

This method efficiently packs the tree into the minimum possible space.

Calculation:

Determine the tree size before writing:

• Tree-size = 10 * NUMBER_OF_CHARACTERS - 1
• Encoded-size = Sum(frequency * length of path to character)

Encoding and Decoding:

• Encoding: Use the proposed bit-wise encoding strategy (see pseudo-code).
• Decoding: Read bit to determine leaf/non-leaf node; if leaf, read value; if non-leaf, recursively decode children.

Example:

For the input string "AAAAABCCCCCCDDEEEEE", the tree can be represented as:

      20
  ----------
  |        8
  |     -------
 12     |     3
-----   |   -----
A   C   E   B   D
6   6   5   1   2

The resulting bit-wise encoding is:

001A1C01E01B1D 0000000000001100101010101011111111010101010

This representation efficiently stores both the tree and the encoded data, resulting in a smaller output compared to the original string.

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