Optimal all-ports collective communication algorithms for the k-ary n-cube interconnection networks

The need for collective communication procedures such as One-to-All broadcast, All-to-All broadcast arises in many parallel or distributed applications. Many of these communication procedures have been studied for many topologies of interconnection networks such as hypercubes, meshes, De Bruijn, star graphs and butterflies. In this paper we propose a construction of multiple edge-disjoint spanning trees for the k-ary n-cube which can be used to derive an optimal and fault tolerant broadcasting algorithm. We propose also an optimal All-to-All broadcasting algorithm. We consider the k-ary n-cube as a point-to-point interconnection, using store-and-forward, all-port assumption and a linear communication model.