Hypercube internetwork topology

In computer networking, hypercube networks are a type of network topology used to connect and route data between multiple processing units or computers. Hypercube networks consist of 2^m nodes, which form the vertices of squares to create an internetwork connection. A hypercube is basically a multidimensional mesh network with two nodes in each dimension. Due to similarity, such topologies are usually grouped into a k-ary d-dimensional mesh topology family, where d represents the number of dimensions and k represents the number of nodes in each dimension.

Hypercube interconnection network is formed by connecting N nodes that can be expressed as a power of 2. This means if the network has N nodes it can be expressed as :

${\displaystyle N=2^{m}}$

where m is the number of bits that are required to label the nodes in the network. So, if there are 4 nodes in the network, 2 bits are needed to represent all the nodes in the network. The network is constructed by connecting the nodes that just differ by one bit in their binary representation. This is commonly referred to as Binary labelling. A 3D hypercube internetwork would be a cube with 8 nodes and 12 edges. A 4D hypercube network can be created by duplicating two 3D networks, and adding a most significant bit. The new added bit should be ‘0’ for one 3D hypercube and ‘1’ for the other 3D hypercube. The corners of the respective one-bit changed MSBs are connected to create the higher hypercube network. This method can be used to construct any m-bit represented hypercube with (m-1)-bit represented hypercube.

Routing method for a hypercube network is referred to as E-Cube routing. The distance between two nodes in the network can be given by Hamming weight of (number of ones in) the XOR-operation between their respective binary labels.

The distance between Node 1 (represented as ‘01’) and Node 2 (represented as ‘10’) in the network given by:

${\displaystyle {\mathsf {Hamming\_weight}}(01\oplus 10)={\mathsf {Hamming\_weight}}(11)=2}$

E-Cube routing is a static routing method that employs XY-routing algorithm. This is commonly referred to as Deterministic, Dimension Ordered Routing model. E-Cube routing works by traversing the network in the k^th dimension where k is the least significant non-zero bit in the result of calculating distance.