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.

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.

Figures

Full text

See pages 1-last of finalVersion_localAlgorithms.pdf