Parallelization of the next Closure algorithm for generating the minimum set of implication rules

Abstract

This paper addresses the problem of handling dense contexts of high dimensionality in the number of objects, which is still an open problem in formal concept analysis. The generation of minimal implication basis in contexts with such characteristics is investigated, where the \textit{NextClosure} algorithm is employed in obtaining the rules. Therefore, this work makes use of parallel computing as a means to reduce the prohibitive times observed in scenarios where the input context has high density and high dimensionality. The sequential and parallel versions of the \textit{NextClosure} algorithm applied to generating implications are employed. The experiments show a reduction of approximately 75\% in execution time in the contexts of greater size and density, which attests to the viability of the strategy presented in this work.