Homogeneous and Non Homogeneous Algorithms

TL;DR

This paper introduces a mathematical classification of sorting algorithms into homogeneous and non-homogeneous types, emphasizing the importance of best case analysis alongside worst case in understanding algorithm behavior.

Contribution

It provides a formal mathematical framework to distinguish homogeneous from non-homogeneous algorithms based on their complexity behavior.

Findings

Homogeneous algorithms behave uniformly across all instances.

The classification clarifies the role of best case analysis in algorithm evaluation.

Both classes contain algorithms with varying worst and best case complexities.

Abstract

Motivated by recent best case analyses for some sorting algorithms and based on the type of complexity we partition the algorithms into two classes: homogeneous and non homogeneous algorithms. Although both classes contain algorithms with worst and best cases, homogeneous algorithms behave uniformly on all instances. This partition clarifies in a completely mathematical way the previously mentioned terms and reveals that in classifying an algorithm as homogeneous or not best case analysis is equally important with worst case analysis.