The DOI matches its Crossref record; 8 of the 8 references it cites were found in a registry or an index.
Graph Sparsification by Effective Resistances
Abstract
We present a nearly linear time algorithm that produces high-quality spectral sparsifiers of weighted graphs. Given as input a weighted graph $G=(V,E,w)$ and a parameter $\epsilon>0$, we produce a weighted subgraph $H=(V,\tilde{E},\tilde{w})$ of G such that $|\tilde{E}|=O(n\log n/\epsilon^2)$ and all $x\in\mathbb{R}^V$ satisfy $(1-\epsilon)\sum_{uv\in E}\,(x(u)-x(v))^2w_{uv}\leq\sum_{uv\in\tilde{E}}\,(x(u)-x(v))^2\tilde{w}_{uv}\leq(1+\epsilon)\sum_{uv\in E}\,(x(u)-x(v))^2w_{uv}$. This improves upon the spectral sparsifiers constructed by Spielman and Teng, which had $O(n\log^{c}n)$ edges for some large constant c, and upon the cut sparsifiers of Benczúr and Karger, which only satisfied these inequalities for $x\in\{0,1\}^V$. A key ingredient in our algorithm is a subroutine of independent interest: a nearly linear time algorithm that builds a data structure from which we can query the approximate effective resistance between any two vertices in a graph in $O(\log n)$ time.
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Cites
A new approach to the maximum-flow problem
Goldberg, A. V., & Tarjan, R. E. (1988) · Journal of the ACM · doi:10.1145/48014.61051 · Cited by 1,882
Database-friendly random projections: Johnson-Lindenstrauss with binary coins
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Fast Monte Carlo Algorithms for Matrices II: Computing a Low-Rank Approximation to a Matrix
Drineas, P., Kannan, R., & Mahoney, M. W. (2006) · SIAM Journal on Computing · doi:10.1137/s0097539704442696 · Cited by 552
Fast monte-carlo algorithms for finding low-rank approximations
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Random Vectors in the Isotropic Position
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The electrical resistance of a graph captures its commute and cover times
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Graph Embeddings and Laplacian Eigenvalues
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Cited by
Discrete Signal Processing on Graphs: Sampling Theory
Chen, S., Varma, R., Sandryhaila, A., & Kovacevic, J. (2015) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2015.2469645 · Cited by 666
Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm
Needell, D., Srebro, N., & Ward, R. (2016) · Mathematical Programming · doi:10.1007/s10107-015-0864-7 · Cited by 432
Federated inference and belief sharing
Friston, K. J., Parr, T., Heins, C., Constant, A., Friedman, D., Isomura, T., Fields, C., Verbelen, T., Ramstead, M., Clippinger, J., et al. (2024) · Neuroscience & Biobehavioral Reviews · doi:10.1016/j.neubiorev.2023.105500 · Cited by 30
Metadata
- Authors
- Spielman, D. A., & Srivastava, N.
- Venue
- SIAM Journal on Computing
- Published
- 2011-01
- Volume
- 40
- Issue
- 6
- Pages
- 1913-1926
- ISSN
- 0097-5397 (ISSN-L)
- 1095-7111
- OpenAlex
- W1983193888
- Cited by
- 489
- References
- 8
- FWCI
- 8.07
- Type
- journal article
- Language
- en
- Open access
- closed
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