Locating one pairwise interaction: Three recursive constructions

In a complex component-based system, choices (levels) for components (factors) may interact to cause faults in the system behaviour. When faults may be caused by interactions among few factors at specific levels, covering arrays provide a combinatorial test suite for discovering the presence of faults. While well studied, covering arrays do not enable one to determine the specific levels of factors causing the faults; locating arrays ensure that the results from test suite execution suffice to determine the precise levels and factors causing faults, when the number of such causes is small. Constructions for locating arrays are at present limited to heuristic computational methods and quite specific direct constructions. In this paper three recursive constructions are developed for locating arrays to locate one pairwise interaction causing a fault.