D-H key exchanges are performed from the leaves up to the root. All the nodes are put in a complete binary tree as leaves, with leaves at the 0–level and the root at the d-level. This algorithm can be explained using a complete binary tree to make it more comprehensible. The novelty of this architecture has resulted in several experimental and commercial products such as the Cosmic Cube, Intel iPSC, Ametek System/14, NCUBE/10, Caltech/JPL Mark III, and the Connection Machine. Since several common interconnection topologies such as ring, tree, and mesh can be embedded in a hypercube, the architecture is suitable for both scientific and general-purpose parallel computation. However, the structure is not modularly expandable and expansion involves changing the number of ports per node. There are k alternative paths between any two PEs, which is a good situation from the point of view of fault-tolerance. The total number of PEs in a k‐dimensional hypercube is 2 k and the total number of links and the diameter are 0.5 × 2 k k and k, respectively.

In general, a k‐cube is defined as the structure resulting from two ( k − 1)-cubes after the corresponding nodes of these two ( k − 1)-cubes are connected by links. Two 0-cubes connected by a line form a 1-cube. There is an elegant recursive definition of hypercube. Since each node is representable by k bits, it has k directly connected neighbors. Two nodes in the hypercube are directly connected if their node addresses differ exactly in one bit position.

Ī hypercube is a k‐dimensional cube where each node has k‐bit address and is connected to k other nodes. BASU, in Soft Computing and Intelligent Systems, 2000 Hypercube. The extra nodes of degree 2 have a very small impact on the properties that are of interest to us, and we will therefore restrict ourselves to the case k = n.Ī Cursory Look at Parallel Architectures and Biologically Inspired Computing This will yield a CCC(n, k) network with k2 n nodes. In principle, each cycle may include k nodes with k ≤ n with the additional k – n nodes having a degree of 2. The resulting CCC(n, n) network has n2 n nodes. In general, each node of degree n in the hypercube H n is replaced by a cycle containing n nodes where the degree of every node in the cycle is 3. Each node of degree three in H 3 is replaced by a cycle consisting of three nodes. A CCC network that corresponds to the H 3 hypercube (see Figure 4.9d) is shown in Figure 4.11. An alternative is the Cube-Connected Cycles (CCC) which keeps the degree of a node fixed at three or less. A node must have n ports, which implies that a new node design is required whenever the size of the network increases. However, these are achieved at the price of a high node degree. The hypercube topology has multiple paths between nodes and a low overall diameter of n for a network of 2 n nodes.

Hypercube car