2014
Nearly 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
A 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
2008
Faster approximate lossy generalized flow via interior point algorithms
Daitch S, Spielman D. Faster approximate lossy generalized flow via interior point algorithms. 2008, 451-460. DOI: 10.1145/1374376.1374441.Peer-Reviewed Original ResearchInterior-point algorithmSymmetric M-matricesFlow problemLinear systemsPoint algorithmLinear equationsM-matrixGeneralized maximum flow problemMinimum cost flow problemLinear system solverFast approximation algorithmMaximum flow problemNumber of edgesRatios of integersDiagonally Dominant MatricesSystem solverΕ-approximationOptimal costApproximation algorithmFast algorithmParameter rangeMaximum flowEquationsPrevious algorithmsAlgorithm
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