Handling the Complexity of Computing Maximal Consistent Blocks

The maximal consistent blocks technique, adopted from discrete mathematics, describes the maximal collection of objects, in which all objects are indiscernible in terms of available information. In this paper, we estimate the total possible number of maximal consistent blocks and prove that the number of such blocks may grow exponentially with respect to the number of attributes for incomplete data with "do not care" conditions. Results indicate that the time complexity of some known algorithms for computing maximal consistent blocks has been underestimated so far. Taking into account the complexity, for the practical usage of such blocks, we propose a performance improvement involving the parallelization of the maximal consistent blocks construction method.