A new metric for evaluating the performance and complexity of computer programs: A new approach to the traditional ways of measuring the complexity of algorithms and estimating running times

TL;DR

This paper introduces r-Complexity, a refined asymptotic notation that improves the evaluation of program performance and complexity, offering more nuanced insights than traditional methods, especially for similar algorithms.

Contribution

The paper proposes r-Complexity, a new asymptotic notation that enhances complexity analysis by capturing subtle differences between algorithms within the same class.

Findings

r-Complexity provides better sensitivity in complexity feedback.

It offers more nuanced insights into algorithm performance.

Enhances discrete analysis with architecture-dependent metrics.

Abstract

This paper presents a refined complexity calculus model: r-Complexity, a new asymptotic notation that offers better complexity feedback for similar programs than the traditional Bachmann-Landau notation, providing subtle insights even for algorithms that are part of the same conventional complexity class. The architecture-dependent metric represents an enhancement that provides better sensitivity with respect to discrete analysis.