A Framework for Parallelizing Approximate Gaussian Elimination

In a breakthrough result, Spielman and Teng (2004) developed a nearly-linear time solver for Laplacian linear equations, i.e. equations where the coefficient matrix is symmetric with non-negative diagonals and zero row sums. Since the development of the Spielman-Teng solver, there has been substantial progress, simplifying and improving their result, but obtaining a fast practical, parallel Laplacian solver remains an open problem.