Inapproximability of the Tutte polynomial
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Inapproximability of the Tutte polynomial
Information and Computation
Reliability in layered networks with random link failures
INFOCOM'10 Proceedings of the 29th conference on Information communications
Rapid mixing of subset Glauber dynamics on graphs of bounded tree-width
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Reliability in layered networks with random link failures
IEEE/ACM Transactions on Networking (TON)
The resilience of WDM networks to probabilistic geographical failures
IEEE/ACM Transactions on Networking (TON)
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The classic all-terminal network reliability problem posits a graph, each of whose edges fails independently with some given probability. The goal is to determine the probability that the network becomes disconnected due to edge failures. This problem has obvious applications in the design of communication networks. Since the problem is ${\sharp {\cal P}}$-complete and thus believed hard to solve exactly, a great deal of research has been devoted to estimating the failure probability. In this paper, we give a fully polynomial randomized approximation scheme that, given any n-vertex graph with specified failure probabilities, computes in time polynomial in n and $1/\epsilon$ an estimate for the failure probability that is accurate to within a relative error of $1\pm\epsilon$ with high probability. We also give a deterministic polynomial approximation scheme for the case of small failure probabilities. Some extensions to evaluating probabilities of $k$-connectivity, strong connectivity in directed Eulerian graphs and $r$-way disconnection, and to evaluating the Tutte polynomial are also described. This version of the paper corrects several errata that appeared in the previous journal publication [D. R. Karger, SIAM J. Comput., 29 (1999), pp. 492--514].