2014
Twice-Ramanujan Sparsifiers
Batson J, Spielman D, Srivastava N. Twice-Ramanujan Sparsifiers. SIAM Review 2014, 56: 315-334. DOI: 10.1137/130949117.Peer-Reviewed Original ResearchSpectral sparsifierLaplacian matrixPositive semidefinite matricesNonnegative diagonal matrixNumber of edgesNumber of verticesDeterministic polynomial time algorithmGeneral theoremSemidefinite matricesNonzero entriesPolynomial time algorithmSparse graphsDiagonal matrixQuadratic formSparse approximationSparsifiersWeighted graphReal matricesSpecial caseTime algorithmGraphVerticesMatrixTheoremApproximation
2013
Spectral sparsification of graphs
Batson J, Spielman D, Srivastava N, Teng S. Spectral sparsification of graphs. Communications Of The ACM 2013, 56: 87-94. DOI: 10.1145/2492007.2492029.Peer-Reviewed Original ResearchSpectral sparsificationApproximate maximum flowLinear systemsSpectral approximationLinear time algorithmCombinatorial optimizationGraph sparsificationLinear equationsDominant matricesArbitrary graphsSparse graphsFast solutionUndirected networksFast algorithmDevelopment of algorithmsSparsificationMinimum cutMaximum flowGraphApproximationAlgorithmEquationsOptimizationImportant toolSolution
2011
Electrical flows, laplacian systems, and faster approximation of maximum flow in undirected graphs
Christiano P, Kelner J, Madry A, Spielman D, Teng S. Electrical flows, laplacian systems, and faster approximation of maximum flow in undirected graphs. 2011, 273-282. DOI: 10.1145/1993636.1993674.Peer-Reviewed Original Research