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Recently, there is a huge research effort in the field of parallel computing to solve different real life problems due to the massive use of computing power in all areas of our life. Parallel computing utilizes the power of multiple processing to solve a problem by distributing the problem into independent processors, so each processor executes a specific unit of the problem simultaneously with other processors. Interconnection network is the backbone topology in which the processors are structured. There are many interconnection network topologies, such as Hypercube, Star, Ring, Mesh, etc (Grama, Gupta, Karypis, & Kumar, 2003; Patterson & Hennessy, 2009; Wang & Taher & Heuvel, 2015; Benrais & Baha, 2016).
The binary Hypercube (or the n-cube for short) is considered as one of the most well-known interconnection networks for multi-processors due to its attractive topological properties; e.g. low diameter regular structure, and its capability to exploit communication locality that is required for many parallel mathematical problems’ solving and applications. Many experimental and commercial systems have been use the n-cube interconnection topology including the NCUBE-2, iPSC/2, Cosmic Cube, and SGI Origin 2000 multiprocessor (Grama, et al., 2003).
Hypercube is a well-known interconnection topology that is widely used in parallel computations, routing algorithms, and as a basic structure in many hybrid interconnection networks. A d-dimensional hypercube; n-cube; consists of 2𝑑 nodes (Saad & Schultz, 1988), where each node can be addressed using d bits label. Each node is connected to its neighbors’ nodes if and only if their labels are differing from it in only one bit position. A d-dimensional hypercube consists of two hypercubes of dimension (d-1). The one-dimensional hypercube has two only connected nodes. The two-dimensional hypercube can be constructed by connecting two one-dimensional hypercubes.
The continuous improvements and advancements of the technology motivate researchers to produce new interconnection topologies. Researches started to utilize such technology by structuring new interconnection networks based on clustering and combining a set on interconnection topologies (Zhao, Xiao, & Parhami, 2009; Al-Sadi, 2015).
Mahafzah, Sleit, Hamad, & Abu-Khabeer (2012) introduced a new structured interconnection network under the name of HHC (Hyper Hexa-Cell) based on the topology of hypercube topology structure; HHC has attractive properties such as low diameter, minimum degree, and good scalability in the topology size. HHC is structured by initializing a hexa-cell graph, within the hexa-cell graph three additional edges are added in a way that two edges are used to construct two opposite triangles and the third edge is used to connect the top nodes of the two opposite triangles, A d-dimensional HHC construction based on a hypercube topology, where each node of a hypercube of dimension d-1 replaced by one dimensional HHC graph. Therefore, each one dimensional HHC represents a subgroup in a d-dimensional HHC graph.
The main purpose of a routing algorithm is to rout a message from one node to another within a specific interconnection network topology. A routing algorithm selects the best path to rout from source to destination, and has great impact on network performance.
A More flexible routing algorithm will lead to a better performance. To be more specific, it will lead to an increasing in the network throughput and also a decreasing in the message latency for routing a message from any source node to any destination node via an optimal selected bath (Al-Sadi, 2015).