Modified hypercubes (MHs) have been proposed as building blocks for hypercube-based parallel systems that support the application of incremental growth techniques. In contrast, systems implementing the standard hypercube network cannot be expanded in practice. However, processor allocation for MHs is a more difticult task due to a slight deviation in their topology from that of the standard hyp...

W e introduce a class of graphs which are variants of t h e hypercube graph. M a n y of the properties of this class of graphs are s imilar t o tha t of the hypercube hence, we refer t o t h e m as t h e class of Hypercube-Like ( H L ) graphs/networks. W e show that the hypercube, t h e twisted n-cube [l] and the multiply-twisted cube [2] are members of this class of graphs. W e also propose s ...

Abstract. It is shown how an arbitrary set of points in the hypercube can be Latinized, i.e., can be transformed into a point set that has the Latin hypercube property. The effect of Latinization on the star discrepancy and other uniformity measures of a point set is analyzed. For a few selected but representative point sampling methods, evidence is provided to show that Latinization lowers the...

In order to overcome the drawback of the hypercube that the number of nodes is limited to a power of two, the incrementally extensible hypercube (IEH) graph is derived for an arbitrary number of nodes [12]. In this paper, we first prove that the incomplete hypercube (IH) is a spanning subgraph of IEH. Next, we present a new method to construct an IEH from an IH. From the aspect of graph embeddi...

The problem of embedding graphs into other graphs is much studied in the graph theory. In fact, much effort has been devoted to determining the conditions under which a graph G is a subgraph of a graph H, having a particular structure. An important class to study is the set of graphs which are embeddable into a hypercube. This importance results from the remarkable properties of the hypercube a...

A hypercube parallel computer is a network of processors. each with only local memory. whose activities are coordinated by messages the processors send between themselves. The interconnection network corresponds to the edges of an n -dimensional cube with a processor at each vertex. This paper gives an overview of the hypercube architecture and its relation to other distributed-memory message-p...

We propose a scheme for producing Latin hypercube samples that can enhance any of the existing sampling algorithms in Bayesian networks. We test this scheme in combination with the likelihood weighting algorithm and show that it can lead to a significant improvement in the convergence rate. While performance of sampiing algorithms in general depends on the numerical properties of a network, in ...

We give two combinatorial proofs of a product formula for the number of spanning trees of the n-dimensional hypercube. The first proof is based on the assertion that if one chooses a uniformly random rooted spanning tree of the hypercube and orient each edge from parent to child, then the parallel edges of the hypercube get orientations which are independent of one another. This independence pr...

In this paper, we introduce the hyper-star graph HS(n, k) as a new interconnection network, and discuss its properties such as faulttolerance, scalability, isomorphism, routing algorithm, and diameter. A hyper-star graph has merits when degree × diameter is used as a desirable quality measure of an interconnection network because it has a small degree and diameter. We also introduce a variation...

In massively parallel computers, processors are often connected in a hypercube configuration. Each vertex in the hypercube represents a processor, and each edge represents a communication link. One problem in such a system is avoiding deadlock, a state where there is a cycle of processors, each waiting on the next indefinitely. A second problem is that in a system with many processors, some are...