In this paper, we consider the problem of embedding a given graph into a fixed-size hypercube. This work is related to other recent research on hypercube embedding. In [1], Bhat describes an order IVl log2 IVI algorithm for testing whether a given graph G = (V, E) is exactly an n-cube. Deciding whether a graph has a distance-preserving embedding into a hypercube can be done in polynomial time [...

We provide probabilistic lower bounds for the star discrepancy of Latin hypercube samples. These bounds are sharp in the sense that they match the recent probabilistic upper bounds for the star discrepancy of Latin hypercube samples proved in [M. Gnewuch, N. Hebbinghaus. Discrepancy bounds for a class of negatively dependent random points including Latin hypercube samples. Preprint 2016.]. Toge...

Abstrust The maximum dimensional subcube located in faulty hypercubes is studied in this paper. Most parallel algorithms can be formulated with the dimension n of the hypercube being a parameter of the algorithm. The reconfiguration problem in a hypercube reduces to finding the maximum dimensional fault-free subcube in the hypercube, that is, helps in achieving graceful and the most effective d...

We consider the problem of embedding graphs into hypercubes with minimal congestion. Kim and Lai showed that for a given N-vertex graph G and a hypercube it is NP-complete to determine whether G is embeddable in the hypercube with unit congestion, but G can be embedded with unit congestion in a hypercube of dimension 6log N if the maximum degree of a vertex in G is no more than 6log N . Bha...

A new scalable interconnection topology called the Spanning Multichannel Linked Hypercube (SMLH) is proposed along with an optical implementation methodology that combines both the advantages of free space optics with those of wavelength division multiplexing techniques. The SMLH uses the hypercube topology as a basic building block and connects such building blocks using two-dimensional multic...

Parallel algorithms of the hypercube allocation strategies are considered in this paper. Although the sequential algorithms of various hypercube allocation strategies are easier to implement, their worst case time complexities exponentially increase as the dimension of the hypercube increases. We show that the free processors can be utilized t o perform the allocation jobs in parallel to improv...

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...