Abstract: The balanced hypercube network, which is a novel interconnection network for parallel computation and data processing, is a newly-invented variant of the hypercube. The particular feature of the balanced hypercube is that each processor has its own backup processor and they are connected to the same neighbors. A Hamiltonian bipartite graph with bipartition V0 ∪V1 is Hamiltonian laceab...

This paper describes different schemes for tolerating faults in hypercube multiprocessors. A study of hypercube algorithms reveals that in many cases, the computations that require local communication are mapped onto topologies such as meshes or rings and the hypercube topology is used for global data communication. Therefore, a faulty hypercube needs to be reconfigured to perform both local an...

A new scalable interconnection topology suitable for massively parallel systems called the Spanning Bus Connected Hypercube (SBCH) is proposed. The SBCH uses the hypercube topology as a basic building block and connects such building blocks using multi-dimensional spanning buses. In doing so, the SBCH combines positive features of both the hypercube (small diameter, high connectivity, symmetry,...

Recently, Chan et al. have proposed a new cycle embedding property called balanced pancyclicity [Discrete Applied Mathematics 155(15) (2007) 1971-1978]. For a graph G(V, E) and any two nodes x and y of V, a cycle R contains x and y can be divided into two paths, Pt1 and Pt2, joining x and y such that len(Pt1)len(Pt2), where len() denote the length of the path . A balanced cycle of an even (r...

The directional hypercube (Dcube) which is a cost-effective variation of the traditional binary hypercube is introduced and analyzed in this paper. It employs directional (simple duplex) links only. The Dcube is defined and its key properties are derived including diameter, bandwidth, and connectivity. The diameter is at most 2 greater than that for a hypercube of the same size; the bandwidth i...

In view of providing an explicit representation of the convex hull by listing all the facets, it is interesting to describe the integral feasible region in terms of interior points, i.e. hypercube vertices which are feasible in (1) and such that all their adjacent hypercube vertices are also feasible in (1) and exterior points, for which there is at least one infeasible adjacent hypercube verte...

To embed a ring in a hypercube is to find a Hamiltonian cycle through every node of the hypercube. It is obvious that no 2 n node Hamiltonian cycle exists in an n-dimensional faulty hypercube which has at least one faulty node. However, if a hypercube has faulty links only and the number of faulty links is at most n − 2, at least one 2 n -node Hamiltonian cycle can be found. In this paper, we p...

The Flexible Hypercube FHN is an important variant of the Hypercube Hn and possesses many desirable properties for interconnection networks. This paper proposes a novel algorithm of fault-tolerant method for mapping a mesh network in a Flexible Hypercube. The main results obtained (1) a searching path of a FHN is including approximate to (n+1) nodes, where n= 2 log N ⎢ ⎥ ⎣ ⎦ . Therefore, there ...

 The use of optimal orthogonal array latin hypercube designs is proposed. Orthogonal arrays were proposed for constructing latin hypercube designs by Tang (1993). Such designs generally have better space filling properties than random latin hypercube designs. Even so, these designs do not necessarily fill the space particularly well. As a result, we consider orthogonal-array-based latin...

Dualcube is an interconnection networks that has hypercube-like structure with the capacity to hold much more nodes than the conventional hypercube with the same number of links per node. The motivation of using dualcube as an interconnection network is to mitigate the problem of increasing the number of links in the large-scale hypercube network while keeps most of the topological properties o...