Mass data processing. Algebraic models and methods. Monograph

The monograph is dedicated to the mathematical and algorithmic support of mass data processing based on algebraic models. One of the most common classes of mass processing is considered - processing of highly active structured data. The construction of algebraic models of data and computations, as well as methods for proving their correspondence, are analyzed. Three algebraic systems are studied, which can be used both as data models and computation models. Algebraic and axiomatic methods for proving the correspondence of these models are investigated. Proof of their correspondence is given: homomorphism and isomorphism. The issue of optimizing the processes of mass data processing, represented as algebraic expressions in the proposed algebra models, is raised. Algorithms for the synthesis and optimization of computation of these expressions are described in detail, as well as the method of symmetric horizontal data distribution, ensuring parallel implementation of computation of algebraic expressions and generalization of the block algorithm for parallel matrix multiplication in the case of multiplying multidimensional matrices. Architectures of software-hardware complexes are proposed for efficient parallel implementation of operations in the considered algebra models. A number of real examples illustrating the application of the proposed methods are provided.
For students, graduate students, and teachers of technical and physical-mathematical universities and faculties.