How to Efficiently Store Huffman Trees for Data Compression?

Efficient Huffman Tree Storage for Data Compression

Huffman encoding optimizes data by assigning shorter codes to more frequent characters. To store the constructed Huffman tree, various approaches exist.

Method for Minimizing Tree Size

If the input data is small, a trade-off exists between efficiency and overhead. For larger datasets, consider the following method:

• Do not store frequencies.

• For each node:

  • If it's a leaf node, output 1 bit followed by the character/byte (N bits).
  • If not a leaf node, output 0 bit and encode both child nodes recursively.

Decoding Procedure:

• Read a bit.
• If 1, read the N-bit character/byte and create a leaf node.
• If 0, read the left and right child nodes recursively.

Example

Consider the input "AAAABCCCCCCDDEEEEE."

• Tree:

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

• Paths:

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

• Encoded Output:

  • Tree: 001A1C01E01B1D (49 bits)
  • Data: 000000000000110010101010101111111101010101 (43 bits)
  • Total: 92 bits (12 bytes)

Comparison

Without Huffman encoding:

• 20 characters * 8 bits = 160 bits (20 bytes)

With Huffman encoding:

• 12 bytes overhead

Considerations for Small Data

For smaller input data, an approach that stores the frequencies might be more space-efficient. Calculate:

• Tree Size = 10 * Number of Characters - 1
• Encoded Size = Sum(Frequency of each character * Length of path to character)

This approach minimizes the probability of wasted space.

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