Using random sampling to find maximum flows in uncapacitated undirected graphs
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Minimum cuts in near-linear time
Journal of the ACM (JACM)
A survey of graph layout problems
ACM Computing Surveys (CSUR)
Cutwidth II: algorithms for partial w-trees of bounded degree
Journal of Algorithms
Graph parameters measuring neighbourhoods in graphs-Bounds and applications
Discrete Applied Mathematics
Efficient Algorithms for the k Smallest Cuts Enumeration
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Compiling a massive, multilingual dictionary via probabilistic inference
ACL '09 Proceedings of the Joint Conference of the 47th Annual Meeting of the ACL and the 4th International Joint Conference on Natural Language Processing of the AFNLP: Volume 1 - Volume 1
Probabilistic Verification and Approximation
Electronic Notes in Theoretical Computer Science (ENTCS)
Cutwidth II: Algorithms for partial w-trees of bounded degree
Journal of Algorithms
Panlingual lexical translation via probabilistic inference
Artificial Intelligence
Efficient traffic loss evaluation for transport backbone networks
Computer Networks: The International Journal of Computer and Telecommunications Networking
Sparse reliable graph backbones
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Counting minimum (s, t)-cuts in weighted planar graphs in polynomial time
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Design is as Easy as Optimization
SIAM Journal on Discrete Mathematics
A general framework for graph sparsification
Proceedings of the forty-third annual ACM symposium on Theory of computing
Sparse reliable graph backbones
Information and Computation
Counting and sampling minimum (s,t)-cuts in weighted planar graphs in polynomial time
Theoretical Computer Science
From balls and bins to points and vertices
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Approximating the statistics of various properties in randomly weighted graphs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Boundary-Optimal triangulation flooding
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
On cutwidth parameterized by vertex cover
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Branch and bound for the cutwidth minimization problem
Computers and Operations Research
Ontology-based access to probabilistic data with OWL QL
ISWC'12 Proceedings of the 11th international conference on The Semantic Web - Volume Part I
Linear algebra and sequential importance sampling for network reliability
Proceedings of the Winter Simulation Conference
Variable Formulation Search for the Cutwidth Minimization Problem
Applied Soft Computing
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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 $\SP$-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.