Solving Directed Laplacian Systems in Nearly-Linear Time through Sparse LU Factorizations

In this paper, we show how to solve directed Laplacian systems in nearly-linear time. Given a linear system in an nxn Eulerian directed Laplacian with m nonzero entries, we show how to compute an epsilon-approximate solution in time O(m log(O(1))(n) log(1/epsilon)). Through reductions from [Cohen et al. FOCS'16], this gives the first near...More