A (Weakly) Polynomial Algorithm for AIVF Coding

TL;DR

This paper introduces a weakly polynomial algorithm for designing maximum cost AIVF codes by framing the problem within a linear programming framework, improving efficiency over previous exponential-time methods.

Contribution

It demonstrates that the problem of designing maximum cost AIVF codes can be solved in weakly polynomial time using linear programming and the Ellipsoid method.

Findings

The problem fits into a linear programming framework.

The algorithm runs in weakly polynomial time.

It improves upon previous exponential-time algorithms.

Abstract

It is possible to improve upon Tunstall coding using a collection of multiple parse trees. The best such results so far are Iwata and Yamamoto's maximum cost AIVF codes. The most efficient algorithm for designing such codes is an iterative one that could run in exponential time. In this paper, we show that this problem fits into the framework of a newly developed technique that uses linear programming with the Ellipsoid method to solve the minimum cost Markov chain problem. This permits constructing maximum cost AIVF codes in (weakly) polynomial time.