Torus interconnect

A torus interconnect is a switch-less network topology for connecting processing nodes in a parallel computer system. In geometry, a torus is created by revolving a circle about an axis coplanar to the circle. While this is a general definition in geometry, the topological properties of this type of shape describes the network topology in its essence. The following images are 1D, and 2D torus. 1D torus is a simple circle, and 2D torus has the shape of a doughnut. The animation below illustrates how a 2D torus is generated from a rectangle by connecting its two pairs of opposite edges. Here the concept of torus is used to describe essentially the beginning and ending of a sequence of nodes are connected, like a doughnut. To better illustrate the concept, and understand what the topology means in network interconnect, we give 3 examples of parallel interconnected nodes using torus topology. At one dimension, a torus topology is equivalent to a ring interconnect network, of a shape of a circle. At 2D, it is equivalent to a 2D mesh, but with extra connection at the edge nodes, which is the definition of 2D torus. 1d torus circle.png|1D torus example, a circle. Toroidal coord.png|2D torus example, a donut. Torus from rectangle.gif| Generating a 2D torus from a 2D rectangle. We can generalize the rule from the figures above. Torus interconnect is a switch-less topology that can be seen as a mesh interconnect with nodes arranged in a rectilinear array of N = 2, 3, or more dimensions, with processors connected to their nearest neighbors, and corresponding processors on opposite edges of the array connected.[1] In this lattice, each node has 2N connections. This topology got the name from the fact that the lattice formed in this way is topologically homogeneous to an N-dimensional torus. The first 3 dimensions of torus network topology are easier to visualize and are described below: 1d torus.png|1D Torus illustration 2d torus.png|2D Torus illustration 3d torus.