The analysis of a nested dissection algorithm
Numerische Mathematik
On the performance of the minimum degree ordering for Gaussian elimination
SIAM Journal on Matrix Analysis and Applications
Topics in optimization and sparse linear systems
Topics in optimization and sparse linear systems
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
Latent semantic indexing: a probabilistic analysis
Journal of Computer and System Sciences - Special issue on the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on principles of database systems
Minimizing Congestion in General Networks
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
A practical algorithm for constructing oblivious routing schemes
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
A polynomial-time tree decomposition to minimize congestion
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
Improved Combinatorial Algorithms for the Facility Location and k-Median Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Polynomial time approximation schemes for geometric k-clustering
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Solving Sparse, Symmetric, Diagonally-Dominant Linear Systems in Time 0(m1.31)
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Support Theory for Preconditioning
SIAM Journal on Matrix Analysis and Applications
On clusterings: Good, bad and spectral
Journal of the ACM (JACM)
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Clustering Large Graphs via the Singular Value Decomposition
Machine Learning
Lower bounds for graph embeddings and combinatorial preconditioners
Proceedings of the sixteenth annual ACM symposium on Parallelism in algorithms and architectures
A column approximate minimum degree ordering algorithm
ACM Transactions on Mathematical Software (TOMS)
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Finding effective support-tree preconditioners
Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures
A new approach to data driven clustering
ICML '06 Proceedings of the 23rd international conference on Machine learning
A linear work, O(n1/6) time, parallel algorithm for solving planar Laplacians
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Euro-Par'07 Proceedings of the 13th international Euro-Par conference on Parallel Processing
ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part I
Spectral methods for matrices and tensors
Proceedings of the forty-second ACM symposium on Theory of computing
Hierarchical Diagonal Blocking and Precision Reduction Applied to Combinatorial Multigrid
Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis
Computer Vision and Image Understanding
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
A fast solver for a class of linear systems
Communications of the ACM
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We consider the problem of decomposing a weighted graph with n vertices into a collection P of vertex disjoint clusters such that, for all clusters C ε P, the graph induced by the vertices in C and the edges leaving C, has conductance bounded below by φ. We show that for planar graphs we can compute a decomposition P such that |P| n/ρ, where ρ is a constant, in O(log n) parallel time with O(n) work. Slightly worse guarantees can be obtained in nearly linear time for graphs that have fixed size minors or bounded genus. We show how these decompositions can be used in the first known linear work parallel construction of provably good preconditioners for the important class of fixed degree graph Laplacians. On a more theoretical note, we present upper bounds on the Euclidean distance of eigenvectors of the normalized Laplacian from the space of vectors which consists of the cluster-wise constant vectors scaled by the square roots of the total incident weights of the vertices.