Using Parameter Mapping to Avoid Forbidden Tuples in a Covering Array

Abstract

This paper addresses an optimization problem that occurs when we try to remove from a covering array (CA) the rows that do not satisfy a given set of constraints. That is, how to minimize the number of rows to be removed? The key observation is that the columns of a CA can be swapped without affecting coverage. This makes it possible to explore different ways to map the parameters involved in the constraints to the columns in the CA, which further allows us to reduce the number of rows that must be removed. In order to find an optimal mapping, our approach maps one parameter at a time and employs a greedy algorithm that tries to minimize the number of rows to be removed at each step. We report several experiments in which we compared our approach to two other approaches, i.e., the identity-based approach, and the random approach. The results show that our approach can remove fewer rows than the other two approaches.