# A Local Prime Factor Decomposition Algorithm for Strong Product Graphs

## TL;DR

This paper introduces a quasi-linear time algorithm for prime factor decomposition of strong product graphs, utilizing a local approach to efficiently identify factors and recognize approximate graph products.

## Contribution

It presents a novel local algorithm for PFD of strong product graphs and extends it to recognize approximate graph products, improving practical applicability.

## Key findings

- Algorithm operates in quasi-linear time.
- Effective in identifying prime and approximate graph products.
- Enhances understanding of graph factorization methods.

## Abstract

This work is concerned with the prime factor decomposition (PFD) of strong product graphs. A new quasi-linear time algorithm for the PFD with respect to the strong product for arbitrary, finite, connected, undirected graphs is derived. Moreover, since most graphs are prime although they can have a product-like structure, also known as approximate graph products, the practical application of the well-known "classical" prime factorization algorithm is strictly limited. This new PFD algorithm is based on a local approach that covers a graph by small factorizable subgraphs and then utilizes this information to derive the global factors. Therefore, we can take advantage of this approach and derive in addition a method for the recognition of approximate graph products.