Fat-trees: universal networks for hardware-efficient supercomputing
IEEE Transactions on Computers
The isoperimetric number of random regular graphs
European Journal of Combinatorics
Approximate counting, uniform generation and rapidly mixing Markov chains
Information and Computation
An optimal synchronizer for the hypercube
SIAM Journal on Computing
The electrical resistance of a graph captures its commute and cover times
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
On sparse spanners of weighted graphs
Discrete & Computational Geometry
Approximating s-t minimum cuts in Õ(n2) time
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Local Graph Partitioning using PageRank Vectors
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Expanders via random spanning trees
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Finding sparse cuts locally using evolving sets
Proceedings of the forty-first annual ACM symposium on Theory of computing
Subgraph sparsification and nearly optimal ultrasparsifiers
Proceedings of the forty-second ACM symposium on Theory of computing
Rumour spreading and graph conductance
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Cover times, blanket times, and majorizing measures
Proceedings of the forty-third annual ACM symposium on Theory of computing
A general framework for graph sparsification
Proceedings of the forty-third annual ACM symposium on Theory of computing
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
Spectral Sparsification of Graphs
SIAM Journal on Computing
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
Spectral sparsification via random spanners
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Graph Sparsification by Effective Resistances
SIAM Journal on Computing
| Hi-index | 48.22 |
Graph sparsification is the approximation of an arbitrary graph by a sparse graph. We explain what it means for one graph to be a spectral approximation of another and review the development of algorithms for spectral sparsification. In addition to being an interesting concept, spectral sparsification has been an important tool in the design of nearly linear-time algorithms for solving systems of linear equations in symmetric, diagonally dominant matrices. The fast solution of these linear systems has already led to breakthrough results in combinatorial optimization, including a faster algorithm for finding approximate maximum flows and minimum cuts in an undirected network.