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Optimal Factorization of Operators by Operators That Are Consistent with the Graph’s Structure

In: Optimization Problems in Graph Theory

Author

Listed:
  • Victoria Goncharenko

    (Taras Shevchenko Kiev National University)

  • Yuri Goncharenko

    (Taras Shevchenko Kiev National University)

  • Sergey Lyashko

    (Taras Shevchenko Kiev National University)

  • Vladimir Semenov

    (Taras Shevchenko Kiev National University)

Abstract

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.

Suggested Citation

  • Victoria Goncharenko & Yuri Goncharenko & Sergey Lyashko & Vladimir Semenov, 2018. "Optimal Factorization of Operators by Operators That Are Consistent with the Graph’s Structure," Springer Optimization and Its Applications, in: Boris Goldengorin (ed.), Optimization Problems in Graph Theory, pages 85-91, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-94830-0_4
    DOI: 10.1007/978-3-319-94830-0_4
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