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Local Prime Factor Decomposition of Approximate Strong Product Graphs: Local Prime Factor Decompositionof Approximate Strong Product Graphs

In practice, graphs often occur as perturbed product structures, so-called approximate graph products. The practical application of the well-known prime factorization algorithms is therefore limited, since
most graphs are prime, although they can have a product-like structure.
This work is concerned with the strong graph product. Since strong product graphs G contain
subgraphs that are itself products of subgraphs of the underlying factors of G, we follow the idea to
develop local approaches that cover a graph by factorizable patches and then use this information to
derive the global factors.
First, we investigate the local structure of strong product graphs and introduce the backbone B(G)
of a graph G and the so-called S1-condition. Both concepts play a central role for determining the
prime factors of a strong product graph in a unique way. Then, we discuss several graph classes,
in detail, NICE, CHIC and locally unrefined graphs. For each class we construct local, quasi-linear
time prime factorization algorithms. Combining these results, we then derive a new local prime
factorization algorithm for all graphs.
Finally, we discuss approximate graph products. We use the new local factorization algorithm to
derive a method for the recognition of approximate graph products. Furthermore, we evaluate the
performance of this algorithm on a sample of approximate graph products.

Identiferoai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:11033
Date22 April 2010
CreatorsHellmuth, Marc
ContributorsStadler, Peter F., Klavžar, Sandi, Universität Leipzig
Source SetsHochschulschriftenserver (HSSS) der SLUB Dresden
LanguageEnglish
Detected LanguageEnglish
Typedoc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text
Rightsinfo:eu-repo/semantics/openAccess

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