Huffman coding as an algorithm to construct chains in partition lattices

TL;DR

This paper interprets Huffman coding within the lattice of partitions, showing how the algorithm's greedy property aligns with maximal chains and linear extensions in the lattice structure.

Contribution

It provides a novel lattice-theoretic interpretation of Huffman coding, connecting it to the structure of partition lattices and linear extensions.

Findings

Huffman coding corresponds to maximal chains in the partition lattice.

Greedy Huffman chains match simple linear extensions.

The lattice perspective offers new insights into Huffman's optimality.

Abstract

The Huffman coding algorithm is interpreted in the lattice of partitions of the source alphabet. Maximal chains in the partition lattice correspond to linear extensions of tree orders, and those among the chains that exhibit a simple greedy property correspond precisely to executions of the Huffman algorithm.