Demystifying Algorithmic Complexities and Geometric Review of the 'h'-Index

TL;DR

This paper analyzes the algorithmic complexity of calculating the h-index, reviews geometric methods for its determination, and proposes postulates based on case studies to enhance understanding and visualization.

Contribution

It introduces a geometric approach to calculating the h-index, simplifying its complexity analysis and providing visual clarification compared to algebraic methods.

Findings

Geometric method offers clear visualization of h-index calculation

Algebraic and coding techniques effectively analyze h-index complexity

Proposed postulates based on case studies enhance understanding

Abstract

The current discourse delves into the effectiveness of h-index as an author level metric. It further reviews and explains the algorithmic complexity of calculating h-index through algebraic method. To conduct the algebraic analysis propositional algebra, algorithm and coding techniques have been used. Some use cases have been identified with a finite-data-set/set-of-array to demonstrate the coding techniques and for further analysis. Finally, the explanation and calculative complexities to determine the index have been further simplified through geometric method of calculating the h-index using the similar use cases that was used for coding. It is concluded that determination of the h-index using Euclidean geometric method with Cartesian frame of reference provides a through and visual clarification. Finally, a set of postulates has been proposed at the end of the paper, based on the case studies.