Abstract. Online scheduling of parallel jobs is a problem where jobs with unit processing time and integer release times and deadlines are scheduled on a set of processors. Every job requests certain number of processors. In our setting processors are organized as a hypercube and jobs are scheduled on subhypercubes of the hypercube. The objective is to schedule as many jobs as possible between ...

Several methods for reducing the variance in the context of Monte Carlo simulation are based on correlation induction. This includes antithetic variates, Latin hypercube sampling, and randomized version of quasi-Monte Carlo methods such as lattice rules and digital nets, where the resulting estimators are usually weighted averages of several dependent random variables that can be seen as functi...

We study the relationship between the vertices of an up-monotone polyhedron and those of the polytope obtained by truncating it with the unit hypercube. When the original polyhedron has binary vertices, we characterize the vertices of the truncated polytope in terms of the original vertices, prove their integrality, and show the equivalence of adjacencies in either polyhedron. We conclude by ap...

where ν labels a vector xν = (xν1 , . . . , xνk) with components given by: xνi = νi/N. (2.3) That is, we divide our k-dimensional unit hypercube integration region into N equal pieces, evaluate f(x) at a point in each of these pieces, and take the average over all the pieces. As long as things are reasonably well-behaved, this will converge to the true value of the integral as we take more piec...

The traveling salesman problem (TSP) consists of finding the length of the shortest closed tour visiting N "cities". We consider the Euclidean TSP where the cities are distributed randomly and independently in a d-dimensional unit hypercube. Working with periodic boundary conditions and inspired by a remarkable universality in the kth nearest neighbor distribution, we find for the average optim...

The hierarchical hypercube network is suitable for massively parallel systems. The number of links in the hierarchical hypercube network forms a compromise between those of the hypercube and the cube-connected cycles. Recently, some interesting properties of the hierarchical hypercube network were investigated. Since the hierarchical hypercube is bipartite. A bipartite graph is bipancyclic if i...

Using the probability theory-based approach, this paper reveals the equivalence of an arbitrary NPcomplete problem to a problem of checking whether a level set of a specifically constructed harmonic cost function (with all diagonal entries of its Hessian matrix equal to zero) intersects with a unit hypercube in many-dimensional Euclidean space. This connection suggests the possibility that meth...

Sparse arrays are arrays in which the number of non-zero elements is a small fraction of the total number of array elements. This paper presents computer vision algorithms using sparse representations for arrays. The parallel architecture considered is a hypercube. The algorithms can be easily modified for other architectures like the mesh. We assume that the architecture is SIMD, i.e., all PEs...