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We prove that every graph has a spectral sparsifier with a number of edges linear in its number of vertices.
There is a planar graph almost as good as the complete graph
P. Chew · 1986
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Explicit construction of linear sized tolerant networks
Noga Alon and Fan Chung · 1988
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Ramanujan graphs
A. Lubotzky, R. Phillips, and P. Sarnak · 1988
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Explicit group theoretical constructions of combinatorial schemes and their application to the design of expanders and concentrators
G. A. Margulis · 1988
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Lyapunov theorems for operator algebras
C. A. Akemann and J. Anderson · 1991
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On a problem of Kadison and Singer
J. Bourgain and L. Tzafriri · 1991
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On the second eigenvalue of a graph
Alon Nilli · 1991
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Some new asymptotic properties for the zeros of Jacobi, Laguerre, and Hermite polynomials
H. Dette and W. J. Studden · 1995
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Approximating s-t minimum cuts in O(n 2
András A. Benczúr and David R. Karger · 1996
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Matrix Computations, 3rd. Edition
G. H. Golub and C. F. Van Loan · 1996
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Random vectors in the isotropic position
Mark Rudelson · 1999
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Nearly-linear time algorithms for graph partitioning, graph sparsification, and solving linear systems
Daniel A. Spielman and Shang-Hua Teng · 2004
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The Kadison-Singer problem in discrepancy theory
Nik Weaver · 2004
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Expander graphs and their applications
Shlomo Hoory, Nathan Linial, and Avi Wigderson · 2006
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Graph partitioning using single commodity flows
Rohit Khandekar, Satish Rao, and Umesh Vazirani · 2006
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Graph sparsification by effective resistances
Daniel A. Spielman and Nikhil Srivastava · 2008
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Nearly-linear time algorithms for preconditioning and solving symmetric, diagonally dominant linear systems
Daniel A. Spielman and Shang-Hua Teng · 2008
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Spectral sparsification of graphs
Daniel A. Spielman and Shang-Hua Teng · 2008
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Expanders via random spanning trees
Navin Goyal, Luis Rademacher, and Santosh Vempala · 2009
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The Kadison-Singer problem in mathematics and engineering
Peter G. Casazza and Janet C. Tremain · 2006
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