Calculation of the Comparative Efficiency of Algorithms Using a Single Metric

TL;DR

This paper introduces the A1-Score Factor, a new metric designed to evaluate and compare algorithms based on their combined efficiency in optimizing both time and space simultaneously.

Contribution

The paper presents the development, theoretical proof, and graphical implementation of the A1-Score Factor for assessing algorithm efficiency in dual optimization scenarios.

Findings

A1-Score effectively compares algorithms on combined efficiency.

Theoretical validation supports the metric's reliability.

Graphical tools illustrate the metric's application.

Abstract

While time complexity and space complexity of an algorithm helps to determine its efficiency when time or space needs to be optimized respectively, they fail to determine the more efficient algorithm when time and space both need to be optimized simultaneously. This resulted in the development of the A1-Score Factor which solve the problem i.e., helps to find the algorithm which optimizes both time and space simultaneously. The following research paper contains the hypothesis, the proof, the theoretical and the graphical implementation of the A1-Score Factor along with the use cases of the same.