Mathematical Methods for Reducing the Search Space for Solutions in “Big Data” Analysis and Management

This paper addresses mathematical methods to reduce or segment the search space for big data solutions into distinct subspaces with partial solutions. It is achieved by using a data organization structure of “m-tuples based on ordered sets of arbitrary cardinality.” We provide a mathematical description of this structure and review contemporary methodologies to address similar problems. The study highlights how these properties can significantly reduce the analyzed state space and includes graphs that demonstrate changes in data volume within these subspaces. Additionally, we analyze how variations in four specific arguments affect data volume changes and provide an overview of the efficiency gains in resource use from applying the mathematical methods discussed.