A local prime factor decomposition algorithm

作者：Hellmuth Marc^*

来源：Discrete Mathematics, 2011, 311(12): 944-965.

DOI：10.1016/j.disc.2011.02.016

• Strong product graph
• Prime factor decomposition
• Local covering
• Backbone
• Color-continuation
• S1-condition
• S-prime

This work is concerned with the prime factor decomposition (PFD) of strong product graphs. A new quasi-linear time algorithm for the PFD with respect to the strong product for arbitrary, finite, connected, undirected graphs is derived.
Moreover, since most graphs are prime although they can have a product-like structure, also known as approximate graph products, the practical application of the well-known "classical" prime factorization algorithm is strictly limited. This new PFD algorithm is based on a local approach that covers a graph by small factorizable subgraphs and then utilizes this information to derive the global factors. Therefore, we can take advantage of this approach and derive in addition a method for the recognition of approximate graph products.

• 出版日期2011-6-28
• 单位上海生物信息技术研究中心