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
2012
Twice-Ramanujan Sparsifiers
Batson J, Spielman D, Srivastava N. Twice-Ramanujan Sparsifiers. SIAM Journal On Computing 2012, 41: 1704-1721. DOI: 10.1137/090772873.Peer-Reviewed Original Research
2009
Twice-ramanujan sparsifiers
Batson J, Spielman D, Srivastava N. Twice-ramanujan sparsifiers. 2009, 255-262. DOI: 10.1145/1536414.1536451.Peer-Reviewed Original Research
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
2001
Min–max-boundary domain decomposition
Kiwi M, Spielman D, Teng S. Min–max-boundary domain decomposition. Theoretical Computer Science 2001, 261: 253-266. DOI: 10.1016/s0304-3975(00)00143-2.Peer-Reviewed Original ResearchDistributed-memory parallel computersK-SubgraphParallel computing techniquesDomain decompositionAmount of computationMin-maxComputing techniquesParallel computersLarge communicationGraph decompositionNumber of edgesSubgraphsAlgorithmPartitionComputerComputationCommunicationSpecial caseDecomposition amountGraph GMemory loadBoundary sizeDecompositionNumerical system
1998
Min-Max-Boundary Domain Decomposition
Kiwi M, Spielman D, Teng S. Min-Max-Boundary Domain Decomposition. Lecture Notes In Computer Science 1998, 1449: 137-147. DOI: 10.1007/3-540-68535-9_17.Peer-Reviewed Original ResearchDistributed-memory parallel computersParallel computing techniquesDomain decompositionAmount of computationComputing techniquesSubgraphs G1Parallel computersMemory requirementsPartitioning problemGraph decompositionNumber of edgesMin-maxAlgorithmSubgraphsPartitionComputerComputationCommunicationRequirementsSpecial caseDecomposition amountGraph GBoundary sizeDecompositionNumerical system