Tales of Huffman

TL;DR

This paper introduces a new variant of Huffman coding with length restrictions on certain source words, providing an efficient algorithm for optimal solutions.

Contribution

It formulates and solves a Huffman-like coding problem with individual length constraints using a novel dynamic programming approach.

Findings

Developed an efficient dynamic programming algorithm for the constrained Huffman problem.

Provided an integer programming formulation for the problem, broadening its applicability.

Analyzed structural properties of optimal solutions to guide algorithm design.

Abstract

We study the new problem of Huffman-like codes subject to individual restrictions on the code-word lengths of a subset of the source words. These are prefix codes with minimal expected code-word length for a random source where additionally the code-word lengths of a subset of the source words is prescribed, possibly differently for every such source word. Based on a structural analysis of properties of optimal solutions, we construct an efficient dynamic programming algorithm for this problem, and for an integer programming problem that may be of independent interest.