Hypergraph partitioning for the parallel computing of fuzzy differential equations

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.