We consider the problem of Hamiltonian decomposition on the hypercube. It is known that there exist bn=2c edge-disjoint Hamiltonian cycles on a binary n-cube. However, there are still no simple algorithms to construct such cycles. We present some promising results that may lead to a very simple method to obtain the Hamiltonian decomposition. The binary n-cube is equivalent to the Cartesian prod...

We prove new results for approximating the graphic TSP and some related problems. We obtain polynomial-time algorithms with improved approximation guarantees. For the graphic TSP itself, we improve the approximation ratio to 7/5. For a generalization, the connected-T -join problem, we obtain the first nontrivial approximation algorithm, with ratio 3/2. This contains the graphic s-t-path-TSP as ...

We consider adaptive mortar edge element discretizations in the numerical solution of the quasi-stationary limit of Maxwell’s equations, also known as the eddy currents equations, in three space dimensions. The approach is based on the macro-hybrid variational formulation with respect to a geometrically conforming, non overlapping decomposition of the computational domain. Using adaptively gene...

Based on image contents, the better to simulate the process pattern of human eyes vision, an image fusion method that emphasizing edge preserving is proposed. Through wavelet transform, an improved regional cross entropy fusion rule is used for the low-frequency component which reflects approximate contents, the fusion method for incorporation of the maximum morphology edge measuring and weight...

Edge detection is mainly used in image processing, and is used for feature selection and feature extraction. Edge preservation is important in filtering design to avoid the halo artifacts. Edge preserving decomposition of an image can be achieved using a Local Edge Preserving (LEP) filter. This technique is suitable for High Dynamic Range (HDR) images. Here, multi scale decomposition process is...

This study presents a novel approach by using two-dimension Wavelet Transform (2-D WT) to localize the open and short boundary defect candidates on Ball Grid Array (BGA) substrate conduct paths. Once the potential defects are addressed, traditional inspection algorithms can be implemented for further analysis on these defect candidates. Therefore, the defect-detecting scope and inspection effor...

Let G be a subgraph of Kn. The graph obtained from G by replacing each edge with a 3-cycle whose third vertex is distinct from other vertices in the configuration is called a T (G)-triple. An edge-disjoint decomposition of 3Kn into copies of T (G) is called a T (G)-triple system of order n. If, in each copy of T (G) in a T (G)triple system, one edge is taken from each 3-cycle (chosen so that th...

We use an iterative edge decomposition approach, derived from the popular iterative vertex peeling strategy, to globally split each vertex egonet (subgraph induced by a vertex and its neighbors) into a collection of edge-disjoint layers. Each layer is an edge maximal induced subgraph of minimum degree k that determines the layer density. This edge decomposition is derived completely from the ov...

an injective map f : e(g) → {±1, ±2, · · · , ±q} is said to be an edge pair sum labeling of a graph g(p, q) if the induced vertex function f*: v (g) → z − {0} defined by f*(v) = (sigma e∈ev) f (e) is one-one, where ev denotes the set of edges in g that are incident with a vetex v and f*(v (g)) is either of the form {±k1, ±k2, · · · , ±kp/2} or {±k1, ±k2, · · · , ±k(p−1)/2} u {k(p+1)/2} accordin...

This paper investigates a fully unsupervised statistical method for edge preserving image restoration and compression using a spatial decomposition scheme. Smoothed maximum likelihood is used for local estimation of edge pixels from mixture parametric models of local templates. For the complementary smooth part the traditional L2-variational problem is solved in the Fourier domain with Thin Pla...