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 algorithm for the prime factorization of “locally unrefined” graphs with respect to the strong product. To this end we introduce the backbone \(\mathbb{B} (G)\) 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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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Hellmuth, M., Imrich, W., Klöckl, W. et al. Local Algorithms for the Prime Factorization of Strong Product Graphs. Math.Comput.Sci. 2, 653–682 (2009). https://doi.org/10.1007/s11786-009-0073-y
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DOI: https://doi.org/10.1007/s11786-009-0073-y