Fusion Tree Sorting

TL;DR

This paper explains the fusion tree data structure, which enables sorting algorithms with sub-nlgn time complexity, challenging the long-held belief that nlgn is the lower bound for comparison-based sorting.

Contribution

It introduces the fusion tree data structure and demonstrates its role in achieving faster sorting algorithms than traditional comparison-based methods.

Findings

Fusion trees enable sorting in sub-nlgn time complexity.

The paper clarifies misconceptions about the lower bounds of comparison-based sorting.

Provides a detailed explanation of the fusion tree structure.

Abstract

The sorting problem is one of the most relevant problems in computer science. Within the scope of modern computer science it has been studied for more than 70 years. In spite of these facts, new sorting algorithms have been developed in recent years. Among several types of sorting algorithms, some are quicker; others are more economic in relation to space, whereas others insert a few restrictions in relation to data input. This paper is aimed at explaining the fusion tree data structure, which is responsible for the first sorting algorithm with complexity time smaller than nlgn. The nlgn time complexity has led to some confusion and generated the wrong belief in part of the community of being the minimum possible for this type of problem.