Huffman Coding with Letter Costs: A Linear-Time Approximation Scheme

TL;DR

This paper presents a polynomial-time approximation scheme for Huffman coding with non-uniform letter costs, achieving near-optimal solutions efficiently for practical coding scenarios.

Contribution

It introduces a linear-time approximation algorithm for Huffman coding with arbitrary letter costs, extending classical Huffman coding to more complex cost models.

Findings

Provides a (1+epsilon)-approximate solution within specified time bounds

Efficiently handles non-uniform letter costs like Morse code

Achieves polynomial-time complexity for generalized Huffman coding

Abstract

We give a polynomial-time approximation scheme for the generalization of Huffman Coding in which codeword letters have non-uniform costs (as in Morse code, where the dash is twice as long as the dot). The algorithm computes a (1+epsilon)-approximate solution in time O(n + f(epsilon) log^3 n), where n is the input size.