Minimized Embedding of Arbitrary Hamiltonian Graphs in Fault-tolerant Graph and Reconfiguration at Faults. I. One-fault-tolerant Structures

  • Authors:
  • M. F. Karavai

  • Affiliations:
  • Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

  • Venue:
  • Automation and Remote Control
  • Year:
  • 2004

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Abstract

The paper proposed approaches to minimized embedding of the Hamiltonian graphs in the enveloping fault-tolerant graph representing the structural model of a fault-tolerant multiprocessor computer system. Failures are regarded as faults of vertices and/or connections between the graph vertices. Mathematical studies rely on the group-theoretical analysis of the characteristics of system structure. It underlies the proposed unique approach to designing the one-fault-tolerant and k-fault-tolerant structures retaining after reconfiguration the logical structure of the original target graph and, therefore, the compiled code of system tasks. The minimum fault-tolerant solutions were obtained for one-fault-tolerant and k-fault-tolerant cycles, simple and diagonal grids, and other popular structures, including arbitrary Hamiltonian graphs for which solutions are of minimized nature. Consideration was given to the algorithms of reconfiguration after arbitrary single and multiple faults. Restoration after faults is very simple; it is based on small tables of the group of system automorphisms which enable correct restoration of the system “at the level of theorems” without either static or dynamic additional verification of the reconfiguration process.