  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.
