A new representation of graphs and its applications to parallel processing

In this paper, we propose a new presentation of graphs, called the index-permutation (IP) graph model, and apply it to the systematic development of communication-efficient interconnection networks. We derive several new classes of interconnection networks based on IP graphs to achieve the desired properties. We show that the diameters of some classes of IP graphs are optimal within a factor of 1+0(1) given their node degrees. Designs based on IP graphs can balance system resources by appropriately selecting network parameters, thus providing adaptability to future technology and application requirements.