Profiles of covering arrays of strength two

ARTICLE INFO Covering arrays of strength two have been widely studied as combinatorial models of software interaction test suites for pairwise testing. While numerous algorithmic techniques have been developed for the generation of covering arrays with few columns (factors), the construction of covering arrays with many factors and few tests by these techniques is problematic. Random generation techniques can overcome these computational difficulties, but for strength two do not appear to yield a number of tests that is competitive with the fewest known. Consequently, effective construction of covering arrays with many factors and few tests relies on recursive construction techniques. Article history: Received June 10, 2013 Received in revised form October 20, 2013 Accepted November, 15, 2013 Available online December, 01, 2013 Keyword: covering array, interaction testing, direct product, simulated annealing. AMS subject Classification: 05C38. Corresponding author:Charles J. Colbourn. E-mail: [email protected] E-mail: [email protected] Journal of Algorithms and Computation 44 (2013) PP. 31 60 32 C. J. Colbourn / Journal of Algorithms and Computation 44 (2013) PP. 31 60 1 Abstract continued Among these, a standard direct product has been particularly effective. Necessarily, any recursive method results in substantial duplication of coverage of pairs; by reducing this duplication when possible, the number of tests can sometimes be reduced. In order to reduce duplication, two key features of a covering array are exploited: the number of disjoint rows, and its profile (the distribution of flexible positions). First, the direct product construction is extended to employ different numbers of disjoint rows and different profiles. Then combinatorial and computational constructions for covering arrays with different profiles are developed. Finally some applications of the generalized direct product, with the various profiles so produced, are examined. Of key importance is that, quite frequently, the covering array with fewest tests does not arise as a product of ingredients with the fewest tests; rather, the utility of the ingredient depends in a crucial way on its profile.