An Exact Approach to Maximize the Number of Wild Cards in a Covering Array

Covering Arrays CA(N ; t, k, v) are combinatorial structures that can be used to define adequate test suites for software testing. The smaller a CA is, the smaller the number of test cases that will be given to test the functionality of a software component in order to identify possible failures. Due to the fact that the construction of CAs of optimal size is a highly combinatorial problem, several approximated strategies have been developed. Some constructions of these strategies can be further improved through a post optimization process. For example, the wild card profile of a CA is the set of symbols that can be modified without changing the properties that define a CA. It has been shown that some CAs can be reduced by merging rows that contain wild cards. This paper presents a Branch and Bound (B&B) strategy that maximizes the number of wild cards in the profile of an already constructed CA. We identify such profiles in 106 CAs of strength t = 2 and alphabets v from 6 to 25. Also, it is shown that for an specific CA(42; 2, 8, 6) different profiles can be obtained; such profiles vary in the number of wild cards and their distribution in the CA.