Mathematical Methods for Reducing the Space of Analyzed States when Processing Big Data
Keywords:BIG DATA, DATA ORGANIZATIONAL STRUCTURE, ORDERED SET OF ARBITRARY CARDINALITY, M-TUPLES, METHOD FOR REDUCING THE SPACE OF ANALYZED STATES
This paper addresses the problem of creating mathematical methods to optimize time and computing resources when processing Big Data. These methods are based on the proposed data organizational structure called “m-tuples based on ordered sets of arbitrary cardinality”. We formulated certain properties of the given data organizational structure as a consequence of the logical rules applied for the formation of m-tuples. A set of functional dependencies was also derived between m-tuples based on their location in the structure. A graphical interpretation was presented to illustrate the change of dynamics in fractions of operand combinations for which one tuple is a subset of the other. It takes into account the variation in the lengths of operand tuples. We also obtained logical conclusions about the influence of the properties studied and mathematical methods of working with the given structure to minimize the computing resources involved.
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