We provide a monotone non increasing sequence of upper bounds f k (k ≥ 1) converging to the global minimum of a polynomial f on simple sets like the unit hypercube. The novelty with respect to the converging sequence of upper bounds in [J.B. Lasserre, A new look at nonnegativity on closed sets and polynomial optimization, SIAM J. Optim. 21, pp. 864–885, 2010] is that only elementary computation...

It is folklore that the double-rooted complete binary tree is a spanning tree of the hypercube of the same size. Unfortunately, the usual construction of an embedding of a double-rooted complete binary tree into a hypercube does not provide any hint on how this embedding can be extended if each leaf spawns two new leaves. In this paper, we present simple dynamic embeddings of double-rooted comp...

This is a review article on lattice methods for multiple integration over the unit hypercube, with a variance-reduction viewpoint. It also contains some new results and ideas. The aim is to examine the basic principles supporting these methods and how they can be used eeectively for the simulation models that are typically encountered in the area of Management Science. These models can usually ...

Analytic formulas are developed for various types of power and error rates of some closed testing procedures. The formulas involve non-convex regions that may be integrated with high, pre-specified accuracy using available software. The non-convex regions are represented as a union of hyper-rectangles. These regions are transformed to the unit hypercube, then summed, to create an expression for...

In this paper, we study 1-space bounded multi-dimensional bin packing and hypercube packing. A sequence of items arrive over time, each item is a d-dimensional hyperbox (in bin packing) or hypercube (in hypercube packing), and the length of each side is no more than 1. These items must be packed without overlapping into d-dimensional hypercubes with unit length on each side. In d-dimensional sp...

A new class of interconnection networks called the hexcube is proposed. The hexcube is similar to the base-6 generalized hypercube in structure but has a simpler interconnection scheme. The present work shows that the hexcube is vertex symmetric and possesses topological properties similar to those of the hypercube. This implies that the costs of building parallel computers using the hexcube an...

Approximation in solving the infinite two-person non-cooperative games is studied in the paper. An approximation approach with conversion of infinite game into finite one is suggested. The conversion is fulfilled in three stages. Primarily the players’ payoff functions are sampled variously according to the stated requirements to the sampling. These functions are defined on unit hypercube of th...

Using combinatorial methods, we derive several formulas for the volume of convex bodies obtained by intersecting a unit hypercube with a halfspace, or with a hyperplane of codimension 1, or with a flat defined by two parallel hyperplanes. We also describe some of the history of these problems, dating to Pólya’s Ph.D. thesis, and we discuss several applications of these formulas.

We prove a tight lower bound on the asymptotic performance ratio ρ of the bounded space online d-hypercube bin packing problem, solving an open question raised in 2005. In the classic d-hypercube bin packing problem, we are given a sequence of d-dimensional hypercubes and we have an unlimited number of bins, each of which is a d-dimensional unit hypercube. The goal is to pack (orthogonally) the...

We present several novel data communication algorithms for hypercubes. Speci cally, we obtain (1) an algorithm that broadcasts m messages of unit size on a hypercube of size N in optimal time O(m + logN); and (2) algorithms for special cases of computing m pre x sums, also in optimal time O(m + logN). Unlike previous algorithms for performing similar tasks, our schemes require no use of pipelin...