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arXiv · 1705.03823

Local algorithms for the prime factorization of strong product graphs

Marc Hellmuth·Wilfried Imrich·Werner Klöckl·Peter F. Stadler
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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.

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Marc Hellmuth, Wilfried Imrich, Werner Klöckl, Peter F. Stadler. 2017-05-10. Local algorithms for the prime factorization of strong product graphs. https://arxiv.org/abs/1705.03823

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