This paper presents a general framework for the construction of Monte-Carlo algorithms for the solution of enumeration problems. As an application of the general framework, a Monte-Carlo method is constructed for estimating the failure probability of a multiterminal planar network whose edges are subject to independent random failures. The method is guaranteed to be effective when the failure probabilities of the edges are sufficiently small. 0 1985 Academic Fms, Inc. This paper investigates a classic problem in reliability theory: computing the failure probability of a network whose edges are subject to random failure. Efficient solution methods for this problem have been devised only in special cases (Satyanarayana and Wood, 1982; Wood, 1982) and there are strong indications from computational complexity theory that the general problem is intractable (Provan and Ball, 1981; Valiant, 1979) . Building on our previous work on Monte-Carlo algorithms for enumeration and reliability problems (Karp and Luby, 1983,19&T; Luby, 1983) , we present a Monte-Carlo method for the approximate solution of this problem when the network is planar. Our method is guaranteed to be effective when the failure probabilities of the edges are sufficiently small. In the multiterminal network reliability problem one is given an undirected graph, within which certain vertices are designated as terminals.
In REF , a Monte Carlo method is given to estimate the failure probability with random network link states.
Monte-Carlo algorithms for the planar multiterminal network reliability problem
J. Complex.
J. Complex.
Computer Science