Problems and algorithms for covering arrays via set covers

Abstract

In this paper, we explore some connections between covering arrays (CAs) and set covers (SCs) that already existed in the literature, and in some cases we provide new mappings between these structures. In particular, the devised mappings make feasible an interpretation of weighted budgeted CAs (WBCAs) as weighted budgeted SCs. These connections in turn make it possible to reformulate known greedy heuristics for computing mixed-level CAs and evolve new algorithms for WBCA generation. This also enables importing an upper bound on the size or a lower bound on the covered weight of the generated arrays. We further carry out a comparison of a CA generation strategy that has an analogue in the SC world with one developed specifically for CAs.

Moreover, we experiment with several problem instances for CA and WBCA generation, and compare CA solvers versus SC solvers, both in quality of their output size and covered weights, as well as computation time. Our experiments underpin the hypothesis that CA solvers provide solutions of comparable quality to the ones returned by the considered SC solvers, although the latter solvers generally provide solutions of better quality. Nevertheless, CA solvers provide solutions to the respective problem instances much faster.