# Torus interconnect

Diagram of a 3-dimensional torus interconnect. It is not limited to 8 nodes but can consist of any number of nodes in a similar rectilinear array.

A torus interconnect is a network topology for connecting processing nodes in a parallel computer system. It can be visualized 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] The lattice has the topology of an N dimensional torus and each node has 2N connections.

A number of supercomputers on the TOP500 list use three-dimensional torus networks, e.g. IBM's Blue Gene/L and Blue Gene/P, and the Cray XT3.[2] IBM's Blue Gene/Q uses a five-dimensional torus network. Fujitsu's K computer and the PRIMEHPC FX10 use a proprietary six-dimensional torus interconnect called Tofu.[3]

## Visualization

• In a two-dimensional torus interconnect, the nodes are imagined laid out in a two-dimensional rectangular lattice of rows and columns, with each node connected to its 4 nearest neighbors, and corresponding nodes on opposite edges connected. The connection of opposite edges can be visualized by rolling the rectangular array into a "tube" to connect two opposite edges and then bending the "tube" into a torus to connect the other two.
• In a three-dimensional torus interconnect the nodes are imagined in a three-dimensional lattice in the shape of a rectangular prism, with each node connected with its 6 neighbors, with corresponding nodes on opposing faces of the array connected.

Higher-dimensional arrays can't be directly visualized, but each higher dimension adds another pair of nearest neighbor connections to each node.

While long wrap-around links may be the easiest way to visualize the connection topology, in practice, restrictions on cable lengths often make long wrap-around links impractical. Instead, directly connected nodes -- including nodes that the above visualization places on opposite edges of a grid, connected by a long wrap-around link -- are physically placed nearly adjacent to each other in a folded torus network.[4][5][6] Every link in the folded torus network is very short -- almost as short as the nearest-neighbor links in a simple grid interconnect -- and therefore low-latency.[7]