Combinatorica
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Expanders that beat the eigenvalue bound: explicit construction and applications
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Randomized algorithms
Clique partitions, graph compression and speeding-up algorithms
Journal of Computer and System Sciences
Linear-time encodable and decodable error-correcting codes
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Computing vertex connectivity: new bounds from old techniques
Journal of Algorithms
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Using expander graphs to find vertex connectivity
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Undirected ST-connectivity in log-space
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
An o(log2 k)-approximation algorithm for the k-vertex connected spanning subgraph problem
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Removable edges of a spanning tree in 3-connected 3-regular graphs
FAW'07 Proceedings of the 1st annual international conference on Frontiers in algorithmics
Testing 2-vertex connectivity and computing pairs of vertex-disjoint s-t paths in digraphs
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
An overview of algorithms for network survivability
ISRN Communications and Networking
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The (vertex) connectivity κ of a graph is the smallest number of vertices whose deletion separates the graph or makes it trivial. We present the fastest known algorithm for finding κ. For a digraph with n vertices, m edges and connectivity κ the time bound is O((n + min{κ&frac52;, κn¾})m). This improves the previous best bound of O((n + min{κ3, κn&rcub)m). For an undirected graph both of these bounds hold with m replaced by κn. Expander graphs are useful for solving the following subproblem that arises in connectivity computation: A known set R of vertices contains two large but unknown subsets that are separated by some unknown set S of κ vertices; we must find two vertices of R that are separated by S.