2014
An efficient parallel solver for SDD linear systems
Peng R, Spielman D. An efficient parallel solver for SDD linear systems. 2014, 333-342. DOI: 10.1145/2591796.2591832.Peer-Reviewed Original ResearchSystem of equationsEfficient parallel solverLinear systemsLinear equationsLow-stretch spanning treesSDD matrixDominant matricesParallel solverInput matrixSparse matricesFast algorithmPolylogarithmic timeParallel algorithmEquationsFirst parallel algorithmSpanning treeLinear workAlgorithmMatrixSparsifiersSolverInverseSystemNearly Linear Time Algorithms for Preconditioning and Solving Symmetric, Diagonally Dominant Linear Systems
Spielman D, Teng S. Nearly Linear Time Algorithms for Preconditioning and Solving Symmetric, Diagonally Dominant Linear Systems. SIAM Journal On Matrix Analysis And Applications 2014, 35: 835-885. DOI: 10.1137/090771430.Peer-Reviewed Original ResearchDiagonal entriesInverse power methodLinear system solverDominant linear systemsLower asymptotic complexityLinear systemsLinear time algorithmNonzero structureCondition numberSystem solverDominant matricesFiedler vectorNonzero entriesPreconditionerAsymptotic complexityDevelopment of algorithmsRandomized algorithmSpecial casePower methodIntroduction of algorithmsRecursive fashionTime algorithmAlgorithmMatrixSolver
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 toolSolutionA Local Clustering Algorithm for Massive Graphs and Its Application to Nearly Linear Time Graph Partitioning
Spielman D, Teng S. A Local Clustering Algorithm for Massive Graphs and Its Application to Nearly Linear Time Graph Partitioning. SIAM Journal On Computing 2013, 42: 1-26. DOI: 10.1137/080744888.Peer-Reviewed Original ResearchLinear time algorithmMassive graphsTime algorithmLinear system solverRunning timeSubset of verticesLinear systemsSpectral sparsifierLaplacian matrixNumber edgesSparsest cutSystem solverCorresponding eigenvectorsLocal clustering algorithmSmallest eigenvalueDominant matricesClustering algorithmPartitioning algorithmGraph partitioningWhole graphGraph algorithmsLocal algorithmGraphVerticesBetter clusters
2003
Solving Sparse, Symmetric, Diagonally-Dominant Linear Systems in Time $O({m^{1.31}})$
Spielman D, Teng S. Solving Sparse, Symmetric, Diagonally-Dominant Linear Systems in Time $O({m^{1.31}})$. 2003, 416-427. DOI: 10.1109/sfcs.2003.1238215.Peer-Reviewed Original Research