Before revision: We introduce a randomized algorithm, namely  rchol , to construct an approximate Cholesky factorization for a given sparse Laplacian matrix (a.k.a., graph Laplacian).
After revision: We introduce a randomized algorithm, namely  RCHOL , to construct an approximate Cholesky factorization for a given sparse Laplacian matrix (a.k.a., graph Laplacian).