Fast computation of the first discrete homology group

TL;DR

This paper introduces a new algorithm for efficiently computing the first discrete homology group of graphs, demonstrating superior performance over existing methods through tests on various random graph datasets.

Contribution

The paper presents a novel, faster algorithm for computing the first discrete homology group of graphs, improving on prior algorithms in efficiency.

Findings

The new algorithm significantly outperforms existing methods.

Performance tested on diverse random graph datasets.

Demonstrates practical applicability in computational topology.

Abstract

We present a new algorithm for computing the first discrete homology group of a graph. By testing the algorithm on different data sets of random graphs, we find that it significantly outperforms other known algorithms.