An analytically derived vectorized model for application graph mapping in interconnection networks

Application graph mapping is one of the hardest and time-consuming problems in interconnection networks. Although many approaches are targeting the quality of the solution, one fast and accurate algorithm for solving this kind of problem is needed strongly. In this paper, a vectorized model has been introduced to provide an accurate estimation of the mapping solution with a minimum time overhead. This model is based on a theoretical analysis of the distance matrix and average distance in interconnection networks. Simplifying the search space of possible solutions by a novel matrix-to-vector transformation technique made the proposed model more appropriate and applicable to large-scale applications. The final mapping configuration is computed by comparing vectors to obtain linear time-complexity and make a scalable approach for all sizes of input applications. Moreover, the output of the proposed model can be given to the evolutionary algorithms as the initial solution to save several optimization iterations. We performed extensive experiments to evaluate the execution time overhead and quality of solutions for solving mapping problem. Results show that the proposed vectorized model could save the searching time of evolutionary algorithms up to 70%.