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Acknowledgements This work was supported by a collaborative grant of the Austrian FWF
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Again this will be repeated for all vertices and thus the time complexity is
Determining the backbone B(G): we have to check for a particular vertex v ∈ V (G) whether there is a vertex w ∈ N
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e-mail: imrich@unileoben.ac
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das starke Produkt von endlichen Graphen.
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The time complexity of Algorithm 1 is O(|V | · log 2 (∆) · (∆) 6 ). The for-loop is repeated for all backbone vertices
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M AX ← maximal number of prime factors of decomposed neighborhoods
Algorithm 2 determines the colored Cartesian skeleton with respect to its PFD of a given graph G = (V, E) ∈ Υ with bounded maximum degree ∆ in O(|V | 2 · ∆ 10 ) time
G m of G by taking one connected component of the Cartesian skeleton of each color 1
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.
Mathematics in Computer Science – Springer Journals
Published: Dec 7, 2009
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