Modification of the minimum-degree algorithm by multiple elimination
ACM Transactions on Mathematical Software (TOMS)
A multilevel algorithm for partitioning graphs
Supercomputing '95 Proceedings of the 1995 ACM/IEEE conference on Supercomputing
An Approximate Minimum Degree Ordering Algorithm
SIAM Journal on Matrix Analysis and Applications
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
Improving the Run Time and Quality of Nested Dissection Ordering
SIAM Journal on Scientific Computing
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
A linear-time heuristic for improving network partitions
DAC '82 Proceedings of the 19th Design Automation Conference
A Parallel Multistage ILU Factorization Based on a Hierarchical Graph Decomposition
SIAM Journal on Scientific Computing
The university of Florida sparse matrix collection
ACM Transactions on Mathematical Software (TOMS)
PPAM'05 Proceedings of the 6th international conference on Parallel Processing and Applied Mathematics
Euro-Par'06 Proceedings of the 12th international conference on Parallel Processing
Euro-Par'07 Proceedings of the 13th international Euro-Par conference on Parallel Processing
Hypergraph Cuts & Unsupervised Representation for Image Segmentation
Fundamenta Informaticae
Parallel symmetric sparse matrix-vector product on scalar multi-core CPUs
Parallel Computing
Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis
Parallel graph partitioning on multicore architectures
LCPC'10 Proceedings of the 23rd international conference on Languages and compilers for parallel computing
SIAM Journal on Scientific Computing
Hypergraph Partitioning-Based Fill-Reducing Ordering for Symmetric Matrices
SIAM Journal on Scientific Computing
Using shared arrays in message-driven parallel programs
Parallel Computing
Parallelization of multilevel ILU preconditioners on distributed-memory multiprocessors
PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume Part I
Fast balanced partitioning is hard even on grids and trees
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Euro-Par'07 Proceedings of the 13th international Euro-Par conference on Parallel Processing
Investigation of load balancing scalability in space plasma simulations
PARA'12 Proceedings of the 11th international conference on Applied Parallel and Scientific Computing
Buffer minimization in earliest-deadline first scheduling of dataflow graphs
Proceedings of the 14th ACM SIGPLAN/SIGBED conference on Languages, compilers and tools for embedded systems
Scalable domain decomposition preconditioners for heterogeneous elliptic problems
SC '13 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Patchwork algorithm for the parallel computation of the Green's function in open systems
Journal of Computational Electronics
Scientific Programming - A New Overview of the Trilinos Project --Part 1
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The parallel ordering of large graphs is a difficult problem, because on the one hand minimum degree algorithms do not parallelize well, and on the other hand the obtainment of high quality orderings with the nested dissection algorithm requires efficient graph bipartitioning heuristics, the best sequential implementations of which are also hard to parallelize. This paper presents a set of algorithms, implemented in the PT-Scotch software package, which allows one to order large graphs in parallel, yielding orderings the quality of which is only slightly worse than the one of state-of-the-art sequential algorithms. Our implementation uses the classical nested dissection approach but relies on several novel features to solve the parallel graph bipartitioning problem. Thanks to these improvements, PT-Scotch produces consistently better orderings than ParMeTiS on large numbers of processors.