Nearly-linear time algorithms for graph partitioning, graph sparsification, and solving linear systems

Authors:
Daniel A. Spielman;Shang-Hua Teng
Affiliations:
M.I.T., Cambridge, MA;Boston University, Boston, MA and Akamai Technologies Inc.
Venue:
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Year:
2004

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Abstract

We present algorithms for solving symmetric, diagonally-dominant linear systems to accuracy ε in time linear in their number of non-zeros and log (κf (A) ε), where κf (A) is the condition number of the matrix defining the linear system. Our algorithm applies the preconditioned Chebyshev iteration with preconditioners designed using nearly-linear time algorithms for graph sparsification and graph partitioning.