Augmenting Edge Connectivity via Isolating Cuts
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We give an algorithm for augmenting the edge connectivity of an undirected graph by using the isolating cuts framework (Li and Panigrahi, FOCS '20). Our algorithm uses poly-logarithmic calls to any max-flow algorithm, which yields a running time of Õ(m + n^3/2) and improves on the previous best time of Õ(n^2) (Benczúr and Karger, SODA '98) for this problem. We also obtain an identical improvement in the running time of the closely related edge splitting off problem in undirected graphs.
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