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...

A distance d on a nite set V is hypercube embeddable if it can be isometrically embedded into the hypercube f0; 1g m for some m 1, i.e., if the elements i 2 V can be labeled by sets A i in such a way that d(i; j) = jA i 4A j j for all i; j 2 V. Testing whether a distance d is hypercube embeddable is an NP-complete problem, even if d is assumed to take its values in f2; 3; 4; 6g ((Chv80]). On th...