network reliability measures with binary decision diagrams
Résumé
In this paper, we present a network decomposition method using Binary Decision Diagram (BDD), a state-of-the-art data structure to encode and manipulate boolean functions, for computing the reliability of networks such as computer, communication or power networks. We consider the \textit{so-called} $K$-terminal reliability measure $R_K$ which is defined as the probability that a subset $K$ of nodes can communicate to each other, taking into account the possible failures of the network components (nodes and links). We present an exact algorithm for computing the $K$-terminal reliability of graph $G=(V,E)$ in $O(|E|.F_{max}.2^{F_{max}}.B_{F_{max}})$ where $B_{F_{max}}$ is the Bell number of the maximum boundary set $F_{max}$. Other reliability measures are also discussed. Several examples and experiments show the effectiveness of this approach \footnote{This research was supported by the \emph{Conseil Regional de Picardie}.}.
Loading...