Abstract Huffman Coding and PIFO Tree Embeddings

TL;DR

This paper introduces a generalized Huffman coding algorithm based on monadic structures, unifying Huffman codes and PIFO tree compilation within a common algebraic framework.

Contribution

It develops a unified, monadic approach to Huffman coding that encompasses existing algorithms for Huffman codes and PIFO tree compilation as special cases.

Findings

Unified algebraic framework for Huffman and PIFO algorithms

Generalized Huffman algorithm derived from monadic structures

Potential for broader applications in coding and tree compilation

Abstract

Algorithms for deriving Huffman codes and the recently developed algorithm for compiling PIFO trees to trees of fixed shape (Mohan et al. 2022) are similar, but work with different underlying algebraic operations. In this paper, we exploit the monadic structure of prefix codes to create a generalized Huffman algorithm that has these two applications as special cases.