Worst-case optimal adaptive alphabetic prefix-free coding

TL;DR

This paper introduces the first adaptive alphabetic prefix-free coding algorithm that achieves worst-case optimality in both time and compression for certain alphabet sizes, improving efficiency in data encoding.

Contribution

It presents a novel algorithm that is the first to be worst-case optimal in both time and compression for adaptive alphabetic prefix-free coding under specific alphabet size constraints.

Findings

Achieves worst-case optimality in time and compression

Effective for alphabet sizes smaller than o(n^{1/2}/log n)

Improves adaptive coding efficiency

Abstract

We give the first algorithm for adaptive alphabetic prefix-free coding that is worst-case optimal in terms of time and compression when $\sigma \in o \left( \frac{n^{1 / 2}}{\log n} \right)$, where $\sigma$ is the size of the alphabet and $n$ is the length of the input.