Improved spectral sparsification and numerical algorithms for SDD matrices

Leibniz International Proceedings in Informatics, LIPIcs

Volumn 14, Issue , 2012, Pages 266-277

  Koutis, Ioannis ^a   Levin, Alex ^b   Peng, Richard ^c  

^a UNIVERSITY OF PUERTO RICO   (Puerto Rico)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^c Carnegie Mellon University   (United States)

Author keywords

Linear system solving; Spectral sparsification

Indexed keywords

COMPUTING FUNDAMENTALS; LAPLACIANS; LINEAR SYSTEM SOLVER; LINEAR SYSTEM SOLVING; NUMERICAL ALGORITHMS; SIMPLE MODIFICATIONS; SPARSIFICATION; STRONG APPROXIMATION;

ALGORITHMS; COMPUTER SCIENCE; LINEAR SYSTEMS;

GRAPH THEORY;

EID: 84880318400     PISSN: 18688969     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.4230/LIPIcs.STACS.2012.266     Document Type: Conference Paper

References (14)

1. Ittai Abraham, Yair Bartal, and Ofer Neiman. Nearly tight low stretch spanning trees. CoRR, abs/0808.2017, 2008.
2. Dimitris Achlioptas. Database-friendly random projections. In PODS '01: Proceedings of the Twentieth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, pages 274-281, 2001.
3. 2) time. In STOC '96: Proceedings of the Twenty-Eighth Annual ACM symposium on Theory of Computing, pages 47-55, 1996.
4. Fan Chung. Random walks and local cuts in graphs. Linear Algebra and its applications, 423(1): 22-32, 2007.
5. Wai Shing Fung, Ramesh Hariharan, Nicholas J. A. Harvey, and Debmalya Panigrahi. A general framework for graph sparsification. In STOC '11: Proceedings of the 43rd ACM Symposium on Theory of Computing, pages 71-80, 2011.
6. Piotr Indyk and Rajeev Motwani. Approximate nearest neighbors: towards removing the curse of dimensionality. In STOC '98: Proceedings of the thirtieth annual ACM symposium on Theory of computing, pages 604-613, 1998.
7. Ioannis Koutis, Gary L. Miller, and Richard Peng. Approaching optimality for solving SDD systems. In FOCS '10: Proceedings of the 51st Annual IEEE Symposium on Foundations of Computer Science, 2010.
8. Ioannis Koutis, Gary L. Miller, and Richard Peng. A nearly-m log n solver for SDD linear systems. In FOCS '11: Proceedings of the 52nd Annual IEEE Symposium on Foundations of Computer Science, 2011.
9. Daniel A. Spielman and Nikhil Srivastava. Graph sparsification by effective resistances. In STOC '08: Proceedings of the 40th Annual ACM symposium on Theory of Computing, pages 563-568, 2008.
10. Daniel A. Spielman and Shang-Hua Teng. Nearly-linear time algorithms for graph partitioning, graph sparsification, and solving linear systems. In STOC '04: Proceedings of the 36th Annual ACM Symposium on Theory of Computing, pages 81-90, 2004.
11. Daniel A. Spielman and Shang-Hua Teng. Nearly-linear time algorithms for preconditioning and solving symmetric, diagonally dominant linear systems. CoRR, abs/cs/0607105, 2006.
12. Daniel A. Spielman and Shang-Hua Teng. Spectral sparsification of graphs. CoRR, abs/0808.4134, 2008.
13. Nikhil Srivastava. Spectral sparsification and restricted invertibility, 2010. PhD Thesis, Yale University.
14. Luca Trevisan. Approximation algorithms for unique games. In FOCS '05: Proceedings of the 46th IEEE Symposium on Foundations of Computer Science, pages 5-34, 2005.