Mapping Graphs of Parallel Programs onto Graphs of Distributed Computer Systems by Recurrent Neural Networks

摘要

A problem of mapping graphs of parallel programs onto graphs of distributed computer systems by recurrent neural network is formulated. Parameter values providing absence of incorrect solutions are experimentally determined. Because of introduction of penalty coefficient into Lyapunov function for the program graph edges non-coincided with the system graph edges, optimal solutions are found for mapping a "line"-graph onto a two-dimensional torus. For increasing probability of finding optimal mapping, a method for splitting the mapping is proposed. The method essence is a reducing solution matrix to a block-diagonal form. The Wang recurrent neural network is used to exclude incorrect solutions of the problem of mapping the line-graph onto a three-dimensional torus. This network converges quicker than the Hopfield one.