The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
Spectral Sparsification of Graphs
Open accessAbstract
We introduce a new notion of graph sparsification based on spectral similarity of graph Laplacians: spectral sparsification requires that the Laplacian quadratic form of the sparsifier approximate that of the original. This is equivalent to saying that the Laplacian of the sparsifier is a good preconditioner for the Laplacian of the original. We prove that every graph has a spectral sparsifier of nearly linear size. Moreover, we present an algorithm that produces spectral sparsifiers in time $O(m\log^{c}m)$, where m is the number of edges in the original graph and c is some absolute constant. This construction is a key component of a nearly linear time algorithm for solving linear equations in diagonally dominant matrices. Our sparsification algorithm makes use of a nearly linear time algorithm for graph partitioning that satisfies a strong guarantee: if the partition it outputs is very unbalanced, then the larger part is contained in a subgraph of high conductance.
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Cites
Local Graph Partitioning using PageRank Vectors
Andersen, R., Chung, F., & Lang, K. (2006) · 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06) · doi:10.1109/focs.2006.44 · Cited by 967
Cited by
Han (2023) · doi:10.1109/tpami.2022.3152247 · Cited by 4,682
Big Bird: Transformers for Longer Sequences
Zaheer, M., Guruganesh, G., Dubey, A., Ainslie, J., Alberti, C., Ontanon, S., Pham, P., Ravula, A., Wang, Q., Yang, L., et al. (2020) · arXiv · doi:10.48550/arxiv.2007.14062 · Cited by 1,349
Computational Advertising: Techniques for Targeting Relevant Ads
Woodruff, D. P. (2014) · Foundations and Trends® in Theoretical Computer Science · doi:10.1561/0400000060 · Cited by 866
Spielman, D. A., & Teng, S.-H. (2013) · SIAM Journal on Computing · doi:10.1137/080744888 · Cited by 316
Self-citation
Metadata
- Authors
- Spielman, D. A., & Teng, S.-H.
- Venue
- SIAM Journal on Computing
- Published
- 2011-01
- Volume
- 40
- Issue
- 4
- Pages
- 981-1025
- ISSN
- 0097-5397 (ISSN-L)
- 1095-7111
- OpenAlex
- W2129575457
- Cited by
- 409
- References
- 1
- FWCI
- 12.86
- Type
- journal article
- Language
- en
- Open access
- green
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