The architecture and applications of the class of highly parallel distributed-memory multiprocessors based on the hypercube interconnection structure are surveyed. The history of hypercube computers from their conceptual origins in the 1960s to the recent introduction of commercial machines is briefly reviewed. The properties of hypercube graphs relevant to their use in supercomputers are exami...

The following techniques for uncertainty and sensitivity analysis are briefly summarized: Monte Carlo analysis, differential analysis, response surface methodology, Fourier amplitude sensitivity test, Sobol’ variance decomposition, and fast probability integration. Desirable features of Monte Carlo analysis in conjunction with Latin hypercube sampling are described in discussions of the followi...

We present parallel techniques on hypercubes for solving optimally a class of polygon problems. We thus obtain optimal O(logn)-lime, n-processor hypercube algorithms for the problems of computing the portions of an n-vertex simple polygonal chain C that are visible from a given source point, computing the convex hull of C, testing an n-verlex simple polygon P for monotonicity, and other related...

The hypercube is a particularly versatile network for parallel computing. It is well-known that 2-dimensional grid machines can be simulated on a hypercube with a small constant communication overhead. We introduce new easily computable functions which embed many 3-dimensional grids into their optimal hypercubes with dilation 2. Moreover, we show that one can reduce the open problem to recogniz...

In this paper we review the spectral properties of the hypercube graph Qn and derive the Walsh functions as eigenvectors of the adjacency matrix. We then interpret the Walsh functions as states of the hypercube, with vertices labeled +1 and -1, and elucidate the regularity of the induced vertex neighborhoods and subcubes. We characterize the neighborhoods of each vertex in terms of the number o...

A new, scalable interconnection topology called the Spanning Multichannel Linked Hypercube (SMLH) is proposed. This proposed network is very suitable to massively parallel systems and is highly amenable to optical implementation. The SMLH uses the hypercube topology as a basic building block and connects such building blocks using two-dimensional multichannel links (similar to spanning buses). ...

We show that the hierarchical cubic network, an alternative to the hypercube, is hamiltonian-connected using Gray codes. A network is hamiltonian-connected if it contains a hamiltonian path between every two distinct nodes. In other words, a hamiltonian-connected network can embed a longest linear array between every two distinct nodes with dilation, congestion, load, and expansion equal to one...

Rainbow connection number of Cartesian products and their subgraphs are considered. Previously known bounds are compared and non-existence of such bounds for subgraphs of products are discussed. It is shown that the rainbow connection number of an isometric subgraph of a hypercube is bounded above by the rainbow connection number of the hypercube. Isometric subgraphs of hypercubes with the rain...

Large-Scale multicast applications for the Internet require the availability of multicast protocols that enhance the basic connectionless IP Multicast service. A critical requirement of such protocols is their ability to support a large group of simultaneous users. In this paper, we present a new approach for distributing control information within a multicast group. The goal of our approach is...

We investigate minimax Latin hypercube designs in two dimensions for several distance measures. For the `-distance we are able to construct minimax Latin hypercube designs of n points, and to determine the minimal covering radius, for all n. For the `1-distance we have a lower bound for the covering radius, and a construction of minimax Latin hypercube designs for (infinitely) many values of n....