Partitioning Problems in Parallel, Pipeline, and Distributed Computing
IEEE Transactions on Computers
Computer simulation using particles
Computer simulation using particles
Parallel multigrid in an adaptive PDE solver based on hashing and space-filling curves
Parallel Computing - Special issue on parallelization techniques for numerical modelling
Multilevel algorithms for multi-constraint graph partitioning
SC '98 Proceedings of the 1998 ACM/IEEE conference on Supercomputing
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
The Differencing Method of Set Partitioning
The Differencing Method of Set Partitioning
Fast optimal load balancing algorithms for 1D partitioning
Journal of Parallel and Distributed Computing
SFCGen: A framework for efficient generation of multi-dimensional space-filling curves by recursion
ACM Transactions on Mathematical Software (TOMS)
International Journal of High Performance Computing Applications
Alternative Algorithm for Hilbert's Space-Filling Curve
IEEE Transactions on Computers
OhHelp: a scalable domain-decomposing dynamic load balancing for particle-in-cell simulations
Proceedings of the 23rd international conference on Supercomputing
VECPAR'06 Proceedings of the 7th international conference on High performance computing for computational science
On the metric properties of discrete space-filling curves
IEEE Transactions on Image Processing
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In scientific computing, Space Filling Curves are a widely used tool for one-constraint domain decomposition. They provide a mechanism to sort multi-dimensional data in a locality preserving way, and, in this way, a (one dimensional) list of mesh elements is established which is subsequently split into 3 partitions under consideration of the constraint. This procedure has a runtime of O(NlogN) (N is the number of mesh elements) while nearly perfect load balancing can be established with reasonable partition surface sizes. In this work, we discuss the extensibility of this procedure to two-constraint settings which is desirable, since the methodology is extremely fast. Here, the splitting operation is subject to two constraints, and, unlike to the one-constraint case, obtaining near perfect balancing is often hard to establish, and is, even more as in the one-constraint case, in conflict with the induced surface sizes (or edge-cuts). We discuss multiple strategies to tackle the splitting, and we present a fast, O(NlogN) splitting heuristic algorithm which provides an integer @s that allows to trade off between balancing and surface sizes which results in a O(NlogN) two-constraint decomposition method. Results are compared to the multi-constraint domain decomposition abilities implemented in the Metis software package, and show that the method produces higher surface sizes, but is orders of magnitudes faster which makes the method superior for certain applications.