Fuzzy Sets and Systems - Fuzzy Numbers
On the fuzzy initial value problem
Fuzzy Sets and Systems - Fuzzy Numbers
Parallel iteration of high-order Runge-Kutta methods with stepsize control
Journal of Computational and Applied Mathematics
The Cauchy problem for fuzzy differential equations
Fuzzy Sets and Systems
Combinatorial algorithms for integrated circuit layout
Combinatorial algorithms for integrated circuit layout
Representing circuits more efficiently in symbolic model checking
DAC '91 Proceedings of the 28th ACM/IEEE Design Automation Conference
Parallel and sequential methods for ordinary differential equations
Parallel and sequential methods for ordinary differential equations
Multilevel hypergraph partitioning: application in VLSI domain
DAC '97 Proceedings of the 34th annual Design Automation Conference
Multilevel k-way partitioning scheme for irregular graphs
Journal of Parallel and Distributed Computing
Multilevel hypergraph partitioning: applications in VLSI domain
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
The Cauchy problem for continuous fuzzy differential equations
Fuzzy Sets and Systems
Hypergraph-Partitioning-Based Decomposition for Parallel Sparse-Matrix Vector Multiplication
IEEE Transactions on Parallel and Distributed Systems
Numerical solutions of fuzzy differential equations
Fuzzy Sets and Systems
Existence and uniqueness of solutions to Cauchy problem of fuzzy differential equations
Fuzzy Sets and Systems
Partitioning Rectangular and Structurally Unsymmetric Sparse Matrices for Parallel Processing
SIAM Journal on Scientific Computing
Graph partitioning models for parallel computing
Parallel Computing - Special issue on graph partioning and parallel computing
Petri Nets, Hypergraphs and Conflicts (Preliminary Version)
WG '92 Proceedings of the 18th International Workshop on Graph-Theoretic Concepts in Computer Science
Journal of Parallel and Distributed Computing
SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
Numerical solution of fuzzy differential equations by predictor-corrector method
Information Sciences: an International Journal
First order linear fuzzy differential equations under generalized differentiability
Information Sciences: an International Journal
Parallel Solution of Ordinary Differential Equations
IEEE Transactions on Computers
Note on "Numerical solutions of fuzzy differential equations by predictor-corrector method"
Information Sciences: an International Journal
Comparation between some approaches to solve fuzzy differential equations
Fuzzy Sets and Systems
Generalized receding horizon control of fuzzy systems based on numerical optimization algorithm
IEEE Transactions on Fuzzy Systems
Performance Analysis of Service Composition Based on Fuzzy Differential Equations
IEEE Transactions on Fuzzy Systems
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In our previous work, fuzzy differential equations have been used to describe service composition, and the solutions have been used for the performance analysis. This paper presents a method to compute these fuzzy differential equations in parallel. We first map the underlying Petri net that generates fuzzy differential equations to a hypergraph, and then partition the hypergraph to minimize inter-processor communication while maintaining a good load balance. Based on the partition result, we divide the fuzzy differential equations into several blocks. Finally we design parallel computing algorithm to compute these equations. Software hMETIS is used to partition the hypergraph, and software SUNDIALS is used to support the parallel computing of fuzzy differential equations. Online Shop problem from IBM web site has been used to demonstrate the benefit of our method.