A fast solver for a class of linear systems

Authors:
Ioannis Koutis;Gary L. Miller;Richard Peng
Affiliations:
University of Puerto Rico-Rio Piedras;Carnegie Mellon University;Carnegie Mellon University
Venue:
Communications of the ACM
Year:
2012

Citing 19
Cited 0

A Graph-Theoretic Game and its Application to the $k$-Server Problem

SIAM Journal on Computing
Multigrid

Multigrid
Nearly-linear time algorithms for graph partitioning, graph sparsification, and solving linear systems

STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Lower-stretch spanning trees

Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
The link-prediction problem for social networks

Journal of the American Society for Information Science and Technology
Sampling from large matrices: An approach through geometric functional analysis

Journal of the ACM (JACM)
A linear work, O(n1/6) time, parallel algorithm for solving planar Laplacians

SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Faster approximate lossy generalized flow via interior point algorithms

STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Graph sparsification by effective resistances

STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Graph partitioning into isolated, high conductance clusters: theory, computation and applications to preconditioning

Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
Solving Elliptic Finite Element Systems in Near-Linear Time with Support Preconditioners

SIAM Journal on Numerical Analysis
Breaking the Multicommodity Flow Barrier for O(vlog n)-Approximations to Sparsest Cut

FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Approaching Optimality for Solving SDD Linear Systems

FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
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
Electrical flows, laplacian systems, and faster approximation of maximum flow in undirected graphs

Proceedings of the forty-third annual ACM symposium on Theory of computing
Multigrid and multilevel preconditioners for computational photography

Proceedings of the 2011 SIGGRAPH Asia Conference
Combinatorial preconditioners and multilevel solvers for problems in computer vision and image processing

Computer Vision and Image Understanding
A Nearly-m log n Time Solver for SDD Linear Systems

FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Using petal-decompositions to build a low stretch spanning tree

STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing

Quantified Score

Hi-index	48.22

Visualization

Abstract

The solution of linear systems is a problem of fundamental theoretical importance but also one with a myriad of applications in numerical mathematics, engineering, and science. Linear systems that are generated by real-world applications frequently fall into special classes. Recent research led to a fast algorithm for solving symmetric diagonally dominant (SDD) linear systems. We give an overview of this solver and survey the underlying notions and tools from algebra, probability, and graph algorithms. We also discuss some of the many and diverse applications of SDD solvers.