On the complexity of a fault-tolerance model for multicomputer systems

In topological design of multicomputer systems (e.g., the hypercube), the edge- and vertex-connectivities have traditionally been used as deterministic measures of fault-tolerance. These measures have been noted to have some deficiencies and as a result several generalizations of graph connectivity have been proposed. In this paper, the authors examine some instances of the connectivity generalization proposed by Esfahanian and Hakimi, (1988). This generalization of graph connectivity can be used to model the fault-tolerance analysis of multicomputers in which any set S of the multicomputer components is considered fault free if the set S does not satisfy some given topological property ρ. Using this model and different definitions of ρ, the authors establish the complexity of analyzing the fault-tolerance of multicomputers