A Method for Estimating Minimum Sizes of Covering Arrays Avoiding Forbidden Edges by Decomposing Graphs

Covering Arrays avoiding Forbidden Edges (CAFEs) can be used to detect interaction faults in Systems Under Tests (SUTs), in which certain combinations of factor values are invalid and forbidden. Finding the minimum size of a CAFE has already been proven to be an NP-hard problem, and lower bounds on minimum sizes of CAFEs have been researched. A lower bound on a minimum size of a CAFE with strength two can simply be expressed as a minimum number of pairs to be covered between any two factors. In this paper, a method of Decomposing Graphs based on Forbidden Edges (DGFEs) is proposed to estimate the minimum sizes of CAFEs. This method improves lower bounds on minimum sizes of CAFEs. Lower bounds can be calculated more accurately by the method with vertex subgraphs, which are decomposed from a simple graph based on a certain forbidden edge. Lower bounds calculated using this method can help to verify whether a size of a generated CAFE can be a reality. The experiment results show the feasibility of the DGFE method to some extent in verifying whether generated CAFEs with explicit sizes can be realities.