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Graph based isomorph-free generation of two-level regular fractional factorial designs. (English) Zbl 1178.62082
Summary: We provide a new necessary and sufficient check for testing the isomorphism of two 2-level regular fractional factorial designs. The approach is based on modeling fractional factorial designs as bipartite graphs. We employ an efficient canonical graph labeling approach to compare two designs for isomorphism. We then improve upon the existing non-isomorphic fractional factorial design generation algorithm by reducing the number of candidate designs from which isomorphs need to be removed. Not only does our method generate non-isomorphic designs much faster, it is also able to generate designs with run sizes of 2048 and 4096 runs, which were not generated by the existing methods.

##### MSC:
 62K15 Factorial statistical designs 05C90 Applications of graph theory 65C60 Computational problems in statistics (MSC2010)
nauty; LAPACK
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##### References:
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