Authors S. A. Butenkov
Month, Year 08, 2018 @en
Index UDC 681.332
DOI 10.23683/2311-3103-2018-8-250-262
Abstract The processes of accumulation, compression, storage, extraction, processing and analysis of data are traditionally considered in various sections of theoretical informatics. To solve applied problems of technical implementation of these stages of working with data, methodologically different approaches are used, based on heterogeneous mathematical data models, and, accordingly, technically different software and hardware. At the same time, the optimization of the construction of data processing facilities is considered at each stage separately and using particular mathematical data models. This leads the developers of complex data processing systems to a situation in which, in addition to the actual processing, it is necessary to carry out the processes of converting the data presentation forms for the next stage of processing. Such intermediate conversions of data formats require a significant consumption of hardware resources and time, especially in the case of large amounts of data (Big Data). In a number of our works, a new mathematical apparatus for presenting and processing the data, based on the theory of algebraic systems for granular (integrated) data representation, has been introduced, developed and applied in new computing facilities. The new approach implements the ideas of the granular computing machine introduced by Lotfi Zadeh. It organically includes all the specified stages of working with data (on a uniform mathematical and algorithmic basis) and allows wide use of effective algorithms of linear complexity (greedy algorithms) in tasks related to data storage and processing. A new mathematical representation of data allows the data to be compressed naturally at all stages of processing at the expense of the basic properties of the informational granulation methodology. Since the methods based on the most typed algorithms of granular computations (without cycles and branching) are effectively implemented on reconfigurable high-performance computing systems, the present paper proposes structural solutions for implementing efficient algorithms of processing the granular data in the “fast algorithms”class for the granular computings built by the machines reconfigurable means.

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Keywords Granular computing; reconfigurable computing system; information granulation; matroid; greedy algorithm; algebraical system.
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