The accuracy of the solution to P(XN ) is dependent on the choice of the points XN . Choosing random points can lead to arbitrary bad solutions. To get an accurate solution we resort to optimally mapping a low-discrepancy sequence to the ellipsoidal constraint, which has good equidistribution property. We use a (t,m, s)-net as a starting point on the unit hypercube which is then mapped to the s...

We propose a new heuristic for pure 0–1 programs, which finds feasible integer points by enumerating extended facets of the octahedron, the outer polar of the unit hypercube. We give efficient algorithms to carry out the enumeration, and we explain how our heuristic can be embedded in a branch-and-cut framework. Finally, we present computational results on a set of pure 0–1 programs taken from ...

This paper presents a new construction of homogeneous Dirichlet wavelet basis on the unit interval, linked by diagonal differentiation-integration relation to standard biorthogonal basis. allows compute solution Poisson equation renormalizing coefficients - as in Fourier domain but using locally supported functions with boundary conditions-, which yields linear complexity O(N) for this problem....

Body centered structures are used as seeds for a variety of structures of rank 3 and higher. Propellane based structures are introduced and their design and topological properties are detailed.

We prove that the n-dimensional unit hypercube contains an n-dimensional regular simplex of edge length c √ n, where c > 0 is a constant independent of n. Let l∆n be the n-dimensional regular simplex of edge length l, and let lQn be the n-dimensional hypercube of edge length l. For simplicity, we omit l if l= 1, e.g., Qn denotes the unit hypercube. We are interested in the maximum edge length o...

In this paper we present an optical hypercube-based multichannel network. The hypercube routing functions are implemented on a ring topology using wavelength division multiplexed channels on a single ber. For a network of size N, we show that only r = log 2 N distinct channels are required. This design can accomodate both static and dynamic routing using packet or circuit switching. In addition...

Let // be the integral of f(x) over an A^-dimensional hypercube and Q(m>f be the approximation to //obtained by subdividing the hypercube into m equal subhypercubes and applying the same quadrature rule Q to each. In order to extrapolate efficiently for // on the basis of several different approximations Q ' /, it is necessary to know the form of the error functional Q\m'f If as an expansion in...

An acyclic USO on a hypercube is formed by directing its edges in such as way that the digraph is acyclic and each face of the hypercube has a unique sink and a unique source. A path to the global sink of an acyclic USO can be modeled as pivoting in a unit hypercube of the same dimension with an abstract objective function, and vice versa. In such a way, Zadeh’s ’least entered rule’ and other h...

In this paper, we analysis a hypercube-like structure, called the Folded Hypercube, which is basically a standard hypercube with some extra links established between its nodes. We first show that the n-dimensional folded hypercube is bipartite when n is odd. We also show that the n-dimensional folded hypercube is strongly Hamiltonian-laceable when n is odd, and is Hamiltonian-connected when n =...

In this paper, we analyze a hypercube-like structure, called the folded hypercube, which is basically a standard hypercube with some extra links established between its nodes. We first show that the n-dimensional folded hypercube is bipartite when n is odd.We also show that the n-dimensional folded hypercube is strongly Hamiltonian-laceable when n is odd, and is Hamiltonian-connected when n = 1...