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 $\tilde{O}(m^{\frac{3}{2}-\frac{1}{328}}\log U)$ time.11We use $\tilde{O}(\cdot)$ to suppress logarithmic factors in $m$. For sparse graphs with polynomially bounded integer capacities, this is th...