—We present and evaluate, for the first time, a parallel algorithm for solving the LU decomposition problem on the star graph. The proposed parallel algorithm is of O(N 3 /n!) computation complexity and uses O(Nn) communication time to decompose a matrix of order N on a star graph of dimension n, where N ≥ (n-1)!. The incurred communication time is better than the best known results for the hyp...

We present a silent self-stabilizing distributed algorithm computing a maximal p-star decomposition of the underlying communication network. Under the unfair distributed scheduler, the most general scheduler model, the algorithm converges in at most 12∆m +O(m + n) moves, where m is the number of edges, n is the number of nodes, and ∆ is the maximum node degree. Regarding the move complexity, ou...

<p>With the continuous development of network, scale RDF data is becoming larger and larger. In face large-scale processing, traditional database query method has been unable to meet needs. Due limited characteristics subgraph matching, most existing algorithms often have phenomenon that many subgraphs are repeatedly traversed during process, resulting in a large number intermediate resul...

In the usual forms of homogeneity analysis (which are also known as multiple correspondence analysis or MCA) the size of a point set is defined as the size of the star plot of the set. The star plot is the graph defined by connecting all points in the set with their centroid, and the size is the total squared length of the edges. In order to prevent trivial solutions the configuration X is usua...

From the generating matrix of a linear code one can construct a sequence of generalized star configurations which are strongly connected to the generalized Hamming weights and the underlying matroid of the code. When the code is MDS, the matrix is generic and we obtain the usual star configurations. In our main result, we show that the degree of a generalized star configuration as a projective ...

We describe a program to prove the Kepler conjecture on sphere packings. We then carry out the first step of this program. Each packing determines a decomposition of space into Delaunay simplices, which are grouped together into finite configurations called Delaunay stars. A score, which is related to the density of packings, is assigned to each Delaunay star. We conjecture that the score of ev...

star identification is one of the most important stages in attitude determination with star trackers. this can be performed using matching algorithms between observed stars and a master star catalogue. the main challenge in this approach is to provide a fast and reliable identification algorithm that is sufficiently robust in different pointing views of the star tracker optical system in the sp...

A proper coloring of the vertices of a graph is called a star coloring if the union of every two color classes induce a star forest. The star chromatic number χs(G) is the smallest number of colors required to obtain a star coloring of G. In this paper, we study the relationship between the star chromatic number χs(G) and the maximum average degree Mad(G) of a graph G. We prove that: 1. If G is...

Let L = {H1, H2, . . . ,Hr} be a family of subgraphs of a graph G. An L-decomposition of G is an edge-disjoint decomposition of G into positive integer αi copies of Hi, where i ∈ {1, 2, . . . , r}. Let Ck, Pk and Sk denote a cycle, a path and a star with k edges, respectively. In this paper, we prove that a balanced complete bipartite graph with 2n vertices has a {Ck, Pk, Sk}-decomposition if a...