# Local algorithms for the prime factorization of strong product graphs

## TL;DR

This paper introduces a local, quasi-linear algorithm for prime factorization of strong product graphs, enabling error-tolerant analysis by using graph patches and backbone structures.

## Contribution

It develops a novel local approach using backbone vertices to determine global prime factors in strong product graphs, improving robustness to data noise.

## Key findings

- Algorithm is quasi-linear in complexity
- Backbone neighborhoods suffice for factorization
- Approach enhances error tolerance in graph analysis

## Abstract

The practical application of graph prime factorization algorithms is limited in practice by unavoidable noise in the data. A first step towards error-tolerant "approximate" prime factorization, is the development of local approaches that cover the graph by factorizable patches and then use this information to derive global factors. We present here a local, quasi-linear al- gorithm for the prime factorization of "locally unrefined" graphs with respect to the strong product. To this end we introduce the backbone B(G) for a given graph G and show that the neighborhoods of the backbone vertices provide enough information to determine the global prime factors.