Optimal Factorization of Operators by Operators That Are Consistent with the Graph’s Structure
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In this paper we introduce the notion of an operator that is consistent with the structure of a graph and the computational system that is universal in the class of operators. The model fully corresponds to the processes occurring in distributed computing systems. The problem of the factorization of operators by operators consistent with the structure of a graph is formulated. We prove the criterion for the factorization of a linear invertible operator acting in a finite-dimensional linear space. We obtain upper estimations of the factorization depth of the class of linear invertible operators by linear operators compatible with the structure of the graph.
This research is supported by the Ministry of Education and Science of Ukraine (project 0116U004777). Vladimir Semenov thanks the State Fund for Fundamental Researches of Ukraine for support.
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