Approach to Layouts Used in Toroidal Topologies

Toroidal topologies are shapes following the layout of an n-dimensional torus, whose main feature is the presence of wraparound links along the whole structure. In this paper, three instances of toroidal topologies are studied, such as de Bruijn shapes, k-ary n-cubes and toroidal k-ary grids. De Bruijn shapes of n dimensions are ideal for pattern spotting, as all available patterns of a determined size and alphabet throughout a given shape are located just once. However, k-ary n-cubes and toroidal k-ary grids are ideal for node identification so as to move around them, where the former has a simpler layout, as nodes are labeled in a sequential manner, whilst the latter is more complex to build up, as it minimizes Hamming distance among node identifiers.