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
2007
Spectral partitioning works: Planar graphs and finite element meshes
Spielman D, Teng S. Spectral partitioning works: Planar graphs and finite element meshes. Linear Algebra And Its Applications 2007, 421: 284-305. DOI: 10.1016/j.laa.2006.07.020.Peer-Reviewed Original ResearchBounded-degree planar graphsPlanar graphsSpectral partitioning methodLaplacian matrixSmallest eigenvalueFinite element meshRatio of verticesClass of graphsDimensional meshesElement meshSpectral partitioning techniquesNumerical algorithmFiedler vectorPartitioning methodSmall separatorsTwo-dimensional meshEdge cutGraphSpectral bisectionEigenvaluesPartitioning techniquesMeshBoundsEigenvectorsMatrix
1996
Spectral partitioning works: planar graphs and finite element meshes
Spielman D, Teng S. Spectral partitioning works: planar graphs and finite element meshes. 2011 IEEE 52nd Annual Symposium On Foundations Of Computer Science 1996, 96-105. DOI: 10.1109/sfcs.1996.548468.Peer-Reviewed Original ResearchBounded-degree planar graphsPlanar graphsSpectral partitioning methodLaplacian matrixSmallest eigenvalueFinite element meshRatio of verticesClass of graphsDimensional meshesElement meshSpectral partitioning techniquesNumerical algorithmFiedler vectorPartitioning methodSmall separatorsTwo-dimensional meshEdge cutGraphSpectral bisectionEigenvaluesPartitioning techniquesMeshEigenvectorsBoundsMatrix