Graph sparsification by effective resistances

SIAM Journal on Computing

Volumn 40, Issue 6, 2011, Pages 1913-1926

  Spielman, Daniel A ^a   Srivastava, Nikhil ^a  

^a Yale University   (United States)

Author keywords

Electrical flows; Sparsification; Spectral graph theory

Indexed keywords

ELECTRICAL FLOWS; GRAPH SPARSIFICATION; HIGH QUALITY; LINEAR-TIME ALGORITHMS; SPARSIFICATION; SPECTRAL GRAPH THEORY; SUBGRAPHS; WEIGHTED GRAPH;

ALGORITHMS; DATA STRUCTURES; GRAPHIC METHODS;

GRAPH THEORY;

EID: 84855597147     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/080734029     Document Type: Conference Paper

References (25)

1. D. ACHLIOPTAS, Database-friendly random projections: Johnson- Lindenstrauss with binary coins, J. Comput. System Sci., 66(2003), pp. 671-687.
2. D. ACHLIOPTAS AND F. MCSHERRY, Fast computation of low-rank matrix approximations, J. ACM, 54(2007), article 9.
3. S. ARORA, E. HAZAN, AND S. KALE, A fast random sampling algorithm for sparsifying matrices, in APPROX-RANDOM '06, Lecture Notes in Comput. Sci. 4110, Springer, Berlin, New York, 2006, pp. 272-279. (Pubitemid 44577537)
4. J. D. BATSON, D. A. SPIELMAN, AND N. SRIVASTAVA, Twice-Ramanujan sparsifiers, in Proceedings of the 41st Annual ACM Symposium on Theory of Computing (STOC '09), ACM, New York, 2009, pp. 255-262.
5. 2) time, in Proceedings of the 28th Annual ACM Symposium on Theory of Computing (STOC '96), 1996, pp. 47-55.
6. B. BOLLOBAS, Modern Graph Theory, Springer, Berlin, New York, 1998.
7. A. K. CHANDRA, P. RAGHAVAN, W. L. RUZZO, AND R. SMOLENSKY, The electrical resistance of a graph captures its commute and cover times, Comput. Complexity, 6(1996), pp. 312-340. (Pubitemid 126313289)
8. F. R. K. CHUNG, Spectral Graph Theory, CBMS Regional Conf. Ser. in Math. 92, AMS, Providence, RI, 1997.
9. P. DOYLE AND J. SNELL, Random Walks and Electric Networks, Math. Assoc. America, Washington, DC, 1984.
10. P. DRINEAS AND R. KANNAN, Pass efficient algorithms for approximating large matrices, in Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA '03), ACM, New York, SIAM, Philadelphia, 2003, pp. 223-232.
11. P. DRINEAS, R. KANNAN, AND M. W. MAHONEY, Fast Monte Carlo algorithms for matrices II: Computing a low-rank approximation to a matrix, SIAM J. Comput., 36(2006), pp. 158-183. (Pubitemid 46374022)
12. A. FIRAT, S. CHATTERJEE, AND M. YILMAZ, Genetic clustering of social networks using random walks, Comput. Statist. Data Anal., 51(2007), pp. 6285-6294. (Pubitemid 47126019)
13. F. FOUSS, A. PIROTTE, J.-M. RENDERS, AND M. SAERENS, Random-walk computation of similarities between nodes of a graph with application to collaborative recommendation, IEEE Trans. Knowledge Data Eng., 19(2007), pp. 355-369. (Pubitemid 46374533)
14. A. FRIEZE, R. KANNAN, AND S. VEMPALA, Fast Monte-Carlo algorithms for finding low-rank approximations, J. ACM, 51(2004), pp. 1025-1041. (Pubitemid 40818314)
15. C. GODSIL AND G. ROYLE, Algebraic Graph Theory, Grad. Texts in Math., Springer, Berlin, New York, 2001.
16. A. V. GOLDBERG AND R. E. TARJAN, A new approach to the maximum flow problem, J. ACM, 35(1988), pp. 921-940.
17. S. GUATTERY AND G. L. MILLER, Graph embeddings and Laplacian eigenvalues, SIAM J. Matrix Anal. Appl., 21(2000), pp. 703-723.
18. W. JOHNSON AND J. LINDENSTRAUSS, Extensions of Lipschitz mappings into a Hilbert space, in Modern Analysis and Probability, Contemp. Math. 26, AMS, Providence, RI, 1984, pp. 189-206.
19. R. KHANDEKAR, S. RAO, AND U. VAZIRANI, Graph partitioning using single commodity flows, J. ACM, 56(2009), article 19.
20. G. LUGOSI, Concentration-of-Measure Inequalities, 2003. Available online at http://www.econ. upf.edu/~ lugosi/anu.ps.
21. M. RUDELSON, Random vectors in the isotropic position, J. Funct. Anal., 163(1999), pp. 60-72.
22. M. RUDELSON AND R. VERSHYNIN, Sampling from large matrices: An approach through geometric functional analysis, J. ACM, 54(2007), article 21.
23. D. A. SPIELMAN AND S.-H. TENG, Nearly-linear time algorithms for graph partitioning, graph sparsification, and solving linear systems, in Proceedings of the 36th Annual ACM Symposium on Theory of Computing (STOC '04), 2004, pp. 81-90. Full version available online at http://arxiv.org/abs/cs. DS/0310051.
24. D. A. SPIELMAN AND S.-H. TENG, Nearly-Linear Time Algorithms for Preconditioning and Solving Symmetric, Diagonally Dominant Linear Systems, preprint, 2006. Available online at http://www.arxiv.org/abs/cs. NA/0607105.
25. D. A. SPIELMAN AND S.-H. TENG, Spectral Sparsification of Graphs, preprint, 2008. Available online at http://arxiv.org/abs/0808.4134.