Using the Redundant Chords of the k -Fault-Tolerant Graph to Eliminate the Effect of Failed Components

Abstract

Studies of the structural graphs of the fault-tolerant systems designed by the methods of M.F. Karavai demonstrated that if the number of the redundant graph vertices coincides with the degree k of fault-tolerance, then the number of redundant chords grows rapidly with k. Described was a method of reconfiguration of the redundant graph which is a variant of the sliding redundantization allowing one to use the redundant chords in order to eliminate the effect of some m (> k) failed chords of the graph, its value being dependent on the structure of the objective graph, the magnitude of k, and the topology of failures. Presented were examples of realizing this method which suggest that greater values of m are more frequently obtained for the longest chords of the k-fault-tolerant graph.