On mapping graphs of parallel programs onto graphs of distributed computer systems by recurrent neural networks

A problem of mapping graphs of parallel programs onto graphs of distributed computer systems by recurrent neural networks is formulated. The network parameters providing the absence of incorrect solutions are experimentally determined. By introduction of a penalty coefficient into the Lyapunov function for the program graph edges non-coincided with the edges of the computer system, the optimal solutions are computed for mapping the “line” program graph onto a two-dimensional torus. To increase the optimal solution probability a method of the mapping decomposition is proposed. The method essence is a reduction of the solution matrix to a block-diagonal shape. For exclusion of incorrect solutions in mapping the line onto three-dimensional torus, a recurrent Wang network is used because it is converged more rapidly than the Hopfield network.