41168099
A note on Roman domination in graphs
Let G=(V,E) be a simple graph. A subset [email protected]?V is a dominating set of G, if for any vertex [email protected]?V-S, there exists a vertex [email protected]?S such that [email protected]?E. The domination number of G, @c(G), equals the minimum cardinality of a dominating set. A Roman dominating function on graph G=(V,E) is a function f:V->{0,1,2} satisfying the condition that every vertex v for which f(v)=0 is adjacent to at least one vertex u for which f(u)=2. The weight of a Roman dominating function is the value f(V)[email protected]?"v"@?"Vf(v). The Roman domination number of a graph G, denoted by @c"R(G), equals the minimum weight of a Roman dominating function on G. In this paper, for any integer k(2=
35009889
Tree Domination in Graphs
9838630
Domination in Graphs of Minimum Degree Five
Let G=(V,E) be a simple graph. A subset D⊆V is a dominating set of G, if for any vertex x ∈ V−D, there exists a vertex y ∈ D such that xy ∈ E. By using the so-called vertex disjoint paths cover introduced by Reed, in this paper we prove that every graph G on n vertices with minimum degree at least five has a dominating set of order at most 5n/14.
28317923
Characterization of graphs with equal domination and connected domination numbers
Arumugam and Paulraj Joseph (Discrete Math 206 (1999) 45) have characterized trees, unicyclic graphs and cubic graphs with equal domination and connected domination numbers. In this paper, we extend their results and characterize the class of block graphs and cactus graphs for which the domination number is equal to the connected domination number.
8507685
Global and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalities
The smoothing Newton method for solving a system of nonsmooth equations F(x) = 0, which may arise from the nonlinear complementarity problem, the variational inequality problem or other problems, can be regarded as a variant of the smoothing method. At the kth step, the nonsmooth function F is approximated by a smooth function f(.,∈ κ ), and the derivative of f(.,∈ κ ) at x k is used as the Newton iterative matrix. The merits of smoothing methods and smoothing Newton methods are global convergence and convenience in handling. In this paper, we show that the smoothing Newton method is also superlinearly convergent if F is semismooth at the solution and f satisfies a Jacobian consistency property. We show that most common smooth functions, such as the Gabriel-More function, have this property. As an application, we show that for box constrained variational inequalities if the involved function is P- uniform, the iteration sequence generated by the smoothing Newton method will converge to the unique solution of the problem globally and superlinearly (quadratically).
42417262
On the Minimum Common Integer Partition Problem
We introduce a new combinatorial optimization problem in this paper, called the Minimum Common Integer Partition (MCIP) problem, which was inspired by computational biology applications including ortholog assignment and DNA fingerprint assembly. A partition of a positive integer n is a multiset of positive integers that add up to exactly n, and an integer partition of a multiset S of integers is defined as the multiset union of partitions of integers in S. Given a sequence of multisets S1, ⋯, Sk of integers, where k ≥ 2, we say that a multiset is a common integer partition if it is an integer partition of every multiset Si, 1≤ i≤ k. The MCIP problem is thus defined as to find a common integer partition of S1, ⋯, Sk with the minimum cardinality. It is easy to see that the MCIP problem is NP-hard since it generalizes the well-known Set Partition problem. We can in fact show that it is APX-hard. We will also present a $\frac{5}{4}$-approximation algorithm for the MCIP problem when k = 2, and a $\frac{3k(k-1)}{3k-2}$-approximation algorithm for k ≥ 3.
2587881
Isomap Based on the Image Euclidean Distance
Scientists find that the human perception is based on the similarity on the manifold of data set. Isometric feature mapping (isomap) is one of the representative techniques of manifold. It is intuitive, well understood and produces reasonable mapping results. However, if the input data for manifold learning are corrupted with noises, the isomap algorithm is topologically unstable. In this paper, we present an improved manifold learning method when the input data are images - the image Euclidean distance based isomap (imisomap), in which we use a new distance for images called image Euclidean distance (IMED). Experimental results demonstrate a consistent performance improvement of the algorithm imisomap over the traditional isomap based on Euclidean distance
3226359
Segmentation, Registration, and Deformation Analysis of 3D MR Images of Mice
We demonstrate our mouse MR image and shape analysis pipeline. The long term goal of our work is the description of structural shape variations in normal, genetically identical mice and the subsequent detection of pathological phenotypes in genetically modified mice. The pipeline begins with the acquisition and reconstruction of high resolution MR images of mice. Regions of the images containing organs under study are enhanced via edge-preserving smoothing and mouse organs are segmented using a deformable mesh model. Images are registered using a multi-resolution approach and displacement fields are used to calculate local volume changes. Detailed descriptions and results for each step of the pipeline are presented.
12374753
Efficient Method for Geometric Attribute Estimation
A new method is proposed to estimate the discrete geometric attributes, such as normal vector and curvature. The method contains two steps: points sampling and 4D Shepard interpolation. In the first step, we extract points from point cloud and estimate the attribute of the sampled points. During the second step, we interpolate a global 4D Shepard surface over these sampled points and compute the attribute of each point in point cloud. This method is very effective for using a new global surface model. It benefits many applications such as segmentation, feature extraction, data preprocessing and etc. Application examples are given to verify the proposed method.