Программные средства анализа отказоустойчивости технических систем на основе вершинной целостности графа

Abstract

Nowadays the study of graphs integrity measures is of current interest due to the use of graph models in the design of fault-tolerant complex technical systems. Vertex integrity is one of the determined measures of graph integrity. The system is considered to be ful-ly operational if the corresponding graph is connected. The vertex integrity evaluates the partial loss of system performance due to the com-ponent failure. The graph vertex integrity G = (V, E) is a value of I(G) = min S  V {| S | + w(G – S)}, where w(G – S) is the order of the highest component of the graph connectivity G – S, which is obtained from G by removing all elements belonging to S. The value of w(G – S) char-acterizes the size of the largest fragment of the system, which was formed after the failure of all elements of S. The definition of a vertex in-tegrity of a graph was introduced by Bagga, Barefoot, Entringer and Swart. It is known that the problem of computing I(G) for a general graph is NP-hard. To find the exact value of the vertex integrity we have to know all separators of the graph. This paper presents an algo-rithm and software for finding an approximate value of I(G). The proposed algorithm is limited by considering all minimal separators, there-fore it gives only an upper bound of the vertex integrity. The algorithm labor intensivity polynomially depends on the number of vertices and minimal separators of the input graph. The experimental results showed that the calculated estimates are good and often achievable. When carrying out computational experiments, the exact value of the vertex integrity was received by an exhaustive search of all separators of the input graph.