Preconditioned conjugate gradients for solving singular systems
Journal of Computational and Applied Mathematics - Special issue on iterative methods for the solution of linear systems
Dynamic load balancing for distributed memory multiprocessors
Journal of Parallel and Distributed Computing
A multilevel algorithm for partitioning graphs
Supercomputing '95 Proceedings of the 1995 ACM/IEEE conference on Supercomputing
How Good is Recursive Bisection?
SIAM Journal on Scientific Computing
Multilevel diffusion schemes for repartitioning of adaptive meshes
Journal of Parallel and Distributed Computing - Special issue on dynamic load balancing
Multilevel k-way partitioning scheme for irregular graphs
Journal of Parallel and Distributed Computing
PLUM: parallel load balancing for adaptive unstructured meshes
Journal of Parallel and Distributed Computing
Hypergraph-Partitioning-Based Decomposition for Parallel Sparse-Matrix Vector Multiplication
IEEE Transactions on Parallel and Distributed Systems
An improved diffusion algorithm for dynamic load balancing
Parallel Computing
Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shape-optimized mesh partitioning and load balancing for parallel adaptive FEM
Parallel Computing - Special issue on graph partioning and parallel computing
Parallel optimisation algorithms for multilevel mesh partitioning
Parallel Computing - Special issue on graph partioning and parallel computing
A unified algorithm for load-balancing adaptive scientific simulations
Proceedings of the 2000 ACM/IEEE conference on Supercomputing
Multigrid
Load Balancing in Parallel Computers: Theory and Practice
Load Balancing in Parallel Computers: Theory and Practice
BoomerAMG: a parallel algebraic multigrid solver and preconditioner
Applied Numerical Mathematics - Developments and trends in iterative methods for large systems of equations—in memoriam Rüdiger Weiss
Graph Partitioning and Parallel Solvers: Has the Emperor No Clother? (Extended Abstract)
IRREGULAR '98 Proceedings of the 5th International Symposium on Solving Irregularly Structured Problems in Parallel
Some simplified NP-complete problems
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
A linear-time heuristic for improving network partitions
DAC '82 Proceedings of the 19th Design Automation Conference
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Graph partitioning for high-performance scientific simulations
Sourcebook of parallel computing
Graph Partitioning with the Party Library: Helpful-Sets in Practice
SBAC-PAD '04 Proceedings of the 16th Symposium on Computer Architecture and High Performance Computing
Reducing Complexity in Parallel Algebraic Multigrid Preconditioners
SIAM Journal on Matrix Analysis and Applications
Graph partitioning using single commodity flows
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Graph minimum linear arrangement by multilevel weighted edge contractions
Journal of Algorithms
A combinatorial, primal-dual approach to semidefinite programs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
IEEE Transactions on Knowledge and Data Engineering
Weighted Graph Cuts without Eigenvectors A Multilevel Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
Parallel multilevel algorithms for hypergraph partitioning
Journal of Parallel and Distributed Computing
Advances in Engineering Software
Accelerating shape optimizing load balancing for parallel fem simulations by algebraic multigrid
IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
Balancing parallel adaptive FEM computations by solving systems of linear equations
Euro-Par'05 Proceedings of the 11th international Euro-Par conference on Parallel Processing
Least squares quantization in PCM
IEEE Transactions on Information Theory
Euro-Par'07 Proceedings of the 13th international Euro-Par conference on Parallel Processing
Graph partitioning algorithms for optimizing software deployment in mobile cloud computing
Future Generation Computer Systems
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The NP-hard graph partitioning problem is an important subtask in load balancing and many other applications. It requires the division of a graph's vertex set into P equally sized subsets such that some objective function is optimized. State-of-the-art libraries addressing this problem show several deficiencies: they are hard to parallelize, focus on small edge-cuts instead of few boundary vertices, and often produce disconnected partitions. This work introduces our novel graph partitioning and repartitioning heuristic Bubble-FOS/C. In contrast to other libraries, Bubble-FOS/C does not try to minimize the edge-cut explicitly, but focuses instead implicitly on good partition shapes. The shapes are optimized by diffusion processes that are embedded into an iterative framework. This approach incorporates a high degree of parallelism. Besides describing the evolution process that led to the new diffusion scheme FOS/C used by Bubble-FOS/C, we reveal some of FOS/C's properties and propose a number of enhancements for a fast and reliable implementation. Our experiments, in which we compare sequential and parallel Bubble-FOS/C implementations to the state-of-the-art libraries Metis and Jostle, reveal that our new heuristic is slower, but generates high-quality solutions that are often superior.