A New Algorithm for Building Alphabetic Minimax Trees

TL;DR

This paper introduces an efficient algorithm for constructing alphabetic minimax trees with real weights, significantly improving the computational complexity, and applies it to optimize alphabetic prefix codes based on sample data.

Contribution

It presents a novel algorithm that builds alphabetic minimax trees in nearly optimal time, advancing the efficiency of prefix code construction.

Findings

Algorithm runs in O(n d log log n) time

Efficiently constructs alphabetic minimax trees for real weights

Applied to optimize alphabetic prefix codes from samples

Abstract

We show how to build an alphabetic minimax tree for a sequence (W = w_1, >..., w_n) of real weights in (O (n d \log \log n)) time, where $d$ is the number of distinct integers (\lceil w_i \rceil). We apply this algorithm to building an alphabetic prefix code given a sample.