SUMMARY We develop a balanced, parallel quicksort algorithm for a hypercube and compare it with a similar algorithm for a binary tree machine. The performance of the hypercube algorithm is measured on a Computing Surface.

Given a sequence of n elements, the All Nearest Smaller Values (ANSV) problem is to nd, for each element in the sequence, the nearest element to the left (right) that is smaller, or to report that no such element exists. Time and work optimal algorithms for this problem are known on all the PRAM models 3], 5], but the running time of the best previous hypercube algorithm 6] is optimal only when...

When estimating how much better a classifier is than random allocation in Q-class ROC analysis, we need to sample from a particular region of the unit hypercube: specifically the region, in the unit hypercube, which lies between the Q− 1 simplex in Q(Q− 1) space and the origin. This report introduces a fast method for randomly sampling this volume, and is compared to rejection sampling of unifo...

A &k, d ) hyperpyramid is a level structure of k hypercubes, where the hypercube at level i is of dimension id, and a node at level i 1 is connected to every node in a &dimensional subcube at level i, except for the leaf level k. Hyperpyramids contain pyramids as propy subgraphs. We show that a hyperpyramid P(k, d ) can be embedded in a hypercube with minimal expansion and dilation = d. The con...

Computer experiments are becoming increasingly popular in studying complex real world systems. A special class of sliced Latin hypercube design is proposed in this paper. Such designs are particularly suitable for computer experiments with both qualitative and quantitative factors, multi-fidelity computer experiments, cross-validation and data pooling. The resulting sliced Latin hypercube desig...

Given a sequence of n elements, the All Nearest Smaller Values (ANSV) problem is to nd, for each element in the sequence, the nearest element to the left (right) that is smaller, or to report that no such element exists. Time and work optimal algorithms for this problem are known on all the PRAM models 4, 6], but the running time of the best previous hypercube algorithm 9] is optimal only when ...

Alon and Füredi (1993) showed that the number of hyperplanes required to cover {0,1}n?{0} without covering 0 is n. We initiate study such exact hyperplane covers hypercube for other subsets hypercube. In particular, we provide solutions {0,1}n while missing up four points give asymptotic bounds in general case. Several interesting questions are left open.

In this paper we study diffusion schemes for dynamic load balancing on message passing multiprocessor networks. One of the main results concerns conditions under which these dynamic schemes converge and their rates of convergence for arbitrary topologies. These results use the eigenstructure of the iteration matrices that arise in dynamic load balancing. We completely analyze the hypercube netw...

Various key problems from theoretical computer science can be expressed as polynomial optimization problems over the boolean hypercube. One particularly successful way to prove complexity bounds for these types of problems are based on sums of squares (SOS) as nonnegativity certificates. In this article, we initiate the analysis of optimization problems over the boolean hypercube via a recent, ...

In this paper we modify slightly Razborov’s flag algebras machinery to be suitable for the hypercube. We use this modified method to show that the maximum number of edges of a 4-cycle-free subgraph of the n-dimensional hypercube is at most 0.6068 times the number of its edges. We also improve the upper bound on the number of edges for 6-cycle-free subgraphs of the n-dimensional hypercube from √...