Mathematical Methods for optimizing Big Data Processing

Abstract

This paper addresses the creation and application of mathematical methods to optimize the main characteristics of Big Data. This involves reducing the amount of information processed as well as increasing search speed and processing data while maintaining their respective values and reliability. The foregoing can be achieved by applying the proposed data organization structure called “m-tuples based on ordered sets of arbitrary cardinality”. This ordered structure describes a Boolean template in general. The Boolean template is an ordered set consisting of all subsets of an ordered basis set of arbitrary cardinality and any data type. We conducted a review of modern methodologies used in solving problems of this class. We also describe data organization properties which allow us to predetermine the result of performing certain operations in the structure by its elements using their location without executing a computational algorithm. The graphs represent the “operation of inclusion” when varying the length of the operand tuple. These graphs display the dynamics of changes in the fraction of operand combinations for which one tuple is a subset of the other. We obtained logical conclusions about the influence of the properties and mathematical methods of working with the structure. This allows us to minimize computational resources.