STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Lower bounds for graph embeddings and combinatorial preconditioners
Proceedings of the sixteenth annual ACM symposium on Parallelism in algorithms and architectures
Finding effective support-tree preconditioners
Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures
Algebraic analysis of high-pass quantization
ACM Transactions on Graphics (TOG)
Learning from labeled and unlabeled data on a directed graph
ICML '05 Proceedings of the 22nd international conference on Machine learning
Spectral clustering and transductive learning with multiple views
Proceedings of the 24th international conference on Machine learning
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
Near linear-work parallel SDD solvers, low-diameter decomposition, and low-stretch subgraphs
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
| Hi-index | 0.00 |
We present a linear-system solver that, given an n-by-n symmetric positive semi-definite, diagonally dominant matrix A with m non-zero entries and an n-vector b, produces a vector \tilde x within relative distance \varepsilon of the solution to Ax = b in time 0(m^{1.31} \log ({n \mathord{\left/ {\vphantom {n \varepsilon }} \right. \kern-\nulldelimiterspace} \varepsilon })b^{0(1)}), where b is the log of the ratio of the largest to smallest non-zero entry of A. If the graph of A has genus m^{2\theta } or does not have a K_{m\theta} minor, then the exponent of m can be improved to the minimum of 1 + 5\theta and (9/8)(1 + \theta ). The key contribution of our work is an extension of Vaidya's techniques for constructing and analyzing combinatorial preconditioners.