Fully Dynamic Electrical Flows: Sparse Maxflow Faster Than Goldberg-Rao

We give an algorithm for computing exact maximum flows on graphs with m edges and integer capacities in the range [1, U ] in Õ(m 3 2− 1 328 logU) time.1 For sparse graphs with polynomially bounded integer capacities, this is the first improvement over the Õ(m logU) time bound from [Goldberg-Rao JACM ‘98]. Our algorithm revolves around dynamically maintaining the augmenting electrical flows at the core of the interior point method based algorithm from [Mądry JACM ‘16]. This entails designing data structures that, in limited settings, return edges with large electric energy in a graph undergoing resistance updates. Georgia Institute of Technology, ygao380@gatech.edu Stanford University, yangpliu@stanford.edu Georgia Institute of Technology & University of Waterloo, rpeng@cc.gatech.edu We use Õ(·) to suppress logarithmic factors in m. ar X iv :2 10 1. 07 23 3v 2 [ cs .D S] 1 0 Ju n 20 21

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