Allocating Independent Subtasks on Parallel Processors
IEEE Transactions on Software Engineering
The scattered decomposition for finite elements
Journal of Scientific Computing
SIAM Journal on Scientific and Statistical Computing - Papers from the Second Conference on Parallel Processing for Scientific Computin
Solving problems on concurrent processors
Solving problems on concurrent processors
Discrete event simulations and parallel processing: statistical properties
SIAM Journal on Scientific and Statistical Computing
A mathematical analysis of the scattered decomposition
C3P Proceedings of the third conference on Hypercube concurrent computers and applications: Architecture, software, computer systems, and general issues - Volume 1
Optimal Dynamic Remapping of Data Parallel Computations
IEEE Transactions on Computers
Scalability analysis of partitioning strategies for finite element graphs: a summary of results
Proceedings of the 1992 ACM/IEEE conference on Supercomputing
The cost of conservative synchronization in parallel discrete event simulations
Journal of the ACM (JACM)
Models of machines and computation for mapping in multicomputers
ACM Computing Surveys (CSUR)
Processor allocation in parallel battlefield simulation
WSC '92 Proceedings of the 24th conference on Winter simulation
Profile driven weighted decomposition
ICS '96 Proceedings of the 10th international conference on Supercomputing
An efficient dynamic load balancing algorithm for adaptive mesh refinement
SAC '94 Proceedings of the 1994 ACM symposium on Applied computing
Scalable parallel formulations of the barnes-hut method for n-body simulations
Proceedings of the 1994 ACM/IEEE conference on Supercomputing
Optimal Remapping in Dynamic Bulk Synchronous Computations via a Stochastic Control Approach
IEEE Transactions on Parallel and Distributed Systems
Optimal Remapping in Dynamic Bulk Synchronous Computations via a Stochastic Control Approach
IPDPS '02 Proceedings of the 16th International Parallel and Distributed Processing Symposium
Distributed Simulation with Cellular Automata: Architecture and Applications
SOFSEM '99 Proceedings of the 26th Conference on Current Trends in Theory and Practice of Informatics on Theory and Practice of Informatics
Parallel evolutionary modelling of geological processes
Parallel Computing
PADS '10 Proceedings of the 2010 IEEE Workshop on Principles of Advanced and Distributed Simulation
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A formal analysis of a powerful mapping technique known as scatter decomposition is provided. Scatter decomposition divides an irregular computational domain into a large number of equally sized pieces and distributes them modularly among processors. A probabilistic model of workload in one dimension is used to formally explain why and when scatter decomposition works. The first result is that if a correlation in workload is a convex function of distance, then scattering a more finely decomposed domain yields a lower average processor workload variance. The second result shows that if the workload process is a stationary Gaussian and the correlation function decreases linearly in distance until becoming zero and then remain zero, scattering a more finely decomposed domain yields a lower expected maximum processor workload. It is shown that if the correlation function decreases linearly across the entire domain, then among all mappings that assign an equal number of domain pieces to each processor, scatter decomposition minimizes the average processor workload variance. The dependence of these results on the assumption of decreasing correlation is illustrated with situations where a coarser granularity actually achieves better load balance.