Efficient Algorithm for Computing All Low s-t Edge Connectivities in Directed Graphs

Given a directed graph with n nodes and m edges, the (strong) edge connectivity \(\lambda (u,v)\) between two nodes u and v is the minimum number of edges whose deletion makes u and v not strongly connected. The problem of computing the edge connectivities between all pairs of nodes of a directed graph can be done in \(O(m^\omega )\) time by Cheung, Lau and Leung (FOCS 2011), where \(\omega \) is the matrix multiplication factor (\(\approx 2.373\)), or in \(\tilde{O}(mn^{1.5})\) time using O(n) computations of max-flows by Cheng and Hu (IPCO 1990).

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