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This article addresses the subject of creating mathematical methods in order to optimize time and computing resources when processing “big data.” One of the ways of solving this problem is the creation of NoSQL systems, an advantage of which is the flexibility of data models as well as the possibility of horizontal scaling, parallel processing and the speed of obtaining results. From the viewpoint of “big data” analysis, there have been other methods developed such as machine learning, artificial intelligence, distributed processing of streams and events, and visual data research technology.Furthermore, the aim of the research is to develop mathematical methods for processing “big data” based on the system analysis of the data structure properties known as “m-tuples based on ordered sets of arbitrary cardinality (OSAC).”The data structure “m-tuples based on OSAC” is the Boolean, which is ordered by right-side enumeration of the elements of the basis set with cardinality n from the lower boundary of the possible change of the index value for each element of the tuple to the upper one. We formulated certain properties for the data structure investigated. These properties result from rules of logic when forming this structure. We also described mathematical methods based on these properties. Boolean graphs are illustrated with drawings and the outlined vertices of the graph correspond to the declared properties of the given data structure. We derived analytical dependencies to determine these Boolean elements. These Boolean elements do not require the execution of algorithms that implement the particular operations of intersection, union, and membership because the desired result is already determined by these properties.The properties of the data structure in question with regards to m-tuples based on OSAC allow us to determine some interdependencies between m-tuples by their location in the structure. Their location is determined by a pair of indices (j, m) without executing computing algorithms. In this case, the time estimate for obtaining results changes from a cubic O(n3) to linear O(n) dependency. |
