Solving SDD linear systems in time Õ(mlog nlog(1/ε))

We present an algorithm that on input of an n×n symmetric diagonally dominant matrix A with m non-zero entries constructs in time Õ(m log n) a solver which on input of a vector b computes a vector x satisfying ||x−Ab||A < �||Ab||A in time Õ(m log n log(1/�)) 1. The new algorithm exploits previously unknown structural properties of the output of the incremental sparsification algorithm given in [Koutis,Miller,Peng, FOCS 2010]. We also accelerate the construction of low-stretch spanning trees by rounding the edge weights to ensure that each iteration of the hierarchical star decomposition encounters a small number of distinct edge lengths.