Data-flow algorithms for parallel matrix computation
Communications of the ACM
ScaLAPACK user's guide
Multilevel hypergraph partitioning: application in VLSI domain
DAC '97 Proceedings of the 34th annual Design Automation Conference
Hypergraph-Partitioning-Based Decomposition for Parallel Sparse-Matrix Vector Multiplication
IEEE Transactions on Parallel and Distributed Systems
A hypergraph-partitioning approach for coarse-grain decomposition
Proceedings of the 2001 ACM/IEEE conference on Supercomputing
A Krylov--Schur Algorithm for Large Eigenproblems
SIAM Journal on Matrix Analysis and Applications
HPCN Europe 1996 Proceedings of the International Conference and Exhibition on High-Performance Computing and Networking
A Fine-Grain Hypergraph Model for 2D Decomposition of Sparse Matrices
IPDPS '01 Proceedings of the 15th International Parallel & Distributed Processing Symposium
Parallel Scientific Computation: A Structured Approach Using BSP and MPI
Parallel Scientific Computation: A Structured Approach Using BSP and MPI
An overview of the Trilinos project
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
Anasazi software for the numerical solution of large-scale eigenvalue problems
ACM Transactions on Mathematical Software (TOMS)
On Two-Dimensional Sparse Matrix Partitioning: Models, Methods, and a Recipe
SIAM Journal on Scientific Computing
Multilevel algorithms for partitioning power-law graphs
IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
Site-Based Partitioning and Repartitioning Techniques for Parallel PageRank Computation
IEEE Transactions on Parallel and Distributed Systems
The university of Florida sparse matrix collection
ACM Transactions on Mathematical Software (TOMS)
A scalable eigensolver for large scale-free graphs using 2D graph partitioning
Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis
Hypergraph partitioning for faster parallel pagerank computation
EPEW'05/WS-FM'05 Proceedings of the 2005 international conference on European Performance Engineering, and Web Services and Formal Methods, international conference on Formal Techniques for Computer Systems and Business Processes
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Scalable parallel computing is essential for processing large scale-free (power-law) graphs. The distribution of data across processes becomes important on distributed-memory computers with thousands of cores. It has been shown that two-dimensional layouts (edge partitioning) can have significant advantages over traditional one-dimensional layouts. However, simple 2D block distribution does not use the structure of the graph, and more advanced 2D partitioning methods are too expensive for large graphs. We propose a new two-dimensional partitioning algorithm that combines graph partitioning with 2D block distribution. The computational cost of the algorithm is essentially the same as 1D graph partitioning. We study the performance of sparse matrix-vector multiplication (SpMV) for scale-free graphs from the web and social networks using several different partitioners and both 1D and 2D data layouts. We show that SpMV run time is reduced by exploiting the graph's structure. Contrary to popular belief, we observe that current graph and hypergraph partitioners often yield relatively good partitions on scale-free graphs. We demonstrate that our new 2D partitioning method consistently outperforms the other methods considered, for both SpMV and an eigensolver, on matrices with up to 1.6 billion nonzeros using up to 16,384 cores.