A Systematic Approach to Develop Efficient Complete Exchange Algorithms for Meshes and Tori

Many authors have considered the design of complete exchange algorithms for a variety of multicomputer models, including hypercubes, multidimensional meshes and tori with different port and message switching models. Frequently, algorithms for a given multicomputer architecture cannot be used (or are not efficient) for a different architecture. This paper presents a method which allows the systematic design of complete exchange algorithms for a wide range of multicomputer architectures, including the cases usually considered in the literature and some other architectures that may be interesting in the future. Performance figures obtained by analytical models show that algorithms obtained through the proposed method are efficient for almost all the multicomputer models under consideration and outperform the best known algorithms for a significant range of the problem and system parameters.