Another Asymptotic Notation : "Almost"

TL;DR

The paper introduces a new asymptotic notation called 'Almost' that aims to provide more precise descriptions of algorithm runtimes than traditional notations like Big-Oh, addressing potential communication errors.

Contribution

It proposes a novel asymptotic notation 'Almost' that improves accuracy in describing algorithm complexity over existing notations.

Findings

'Almost' notation offers more precise runtime descriptions.

It reduces ambiguities in asymptotic analysis.

The notation is comparable to Big-Oh and Big Theta.

Abstract

Asymptotic notations are heavily used while analysing runtimes of algorithms. Present paper argues that some of these usages are non trivial, therefore incurring errors in communication of ideas. After careful reconsidera- tion of the various existing notations a new notation is proposed. This notation has similarities with the other heavily used notations like Big-Oh, Big Theta, while being more accurate when describing the order relationship. It has been argued that this notation is more suitable for describing algorithm runtime than Big-Oh.