Supercomputing and grid computing on the verification of covering arrays

The Covering Arrays (CAs) are mathematical objects with minimal coverage and maximum cardinality that are a good tool for the design of experiments. A covering array is an N×k matrix over an alphabet v s.t. each N×k subset contains at least one time each combination from {0,1,…,v−1}t, given a positive integer value t. The process of ensuring that a CA contains each of the vt combinations is called verification of CA. In this paper, we present an algorithm for CA verification and its implementation details in three different computation paradigms: (a) sequential approach (SA); (b) parallel approach (PA); and (c) Grid approach (GA). Four different PAs were compared in their performance of verifying a matrix as a CA; the PA with the best performance was included in a different experimentation where the three paradigms, SA, PA, and GA were compared in a benchmark composed by 45 possible CA instances. The results showed the limitations of the different paradigms when solving the verification of CA problem, and points out the necessity of a Grid approach to solve the problem when the size of a CA grows.