In the Grid computing community, there are several approaches to execute not only single tasks on single Grid resources but also to support workflow schemes that enable the composition and execution of complex Grid applications. The most commonly used workflow model for this purpose is the Directed Acyclic Graph (DAG). Within the establishment of the Fraunhofer Resource Grid, we developed a Gri...

We present a linear time algorithm that constructs a planar polyline grid drawing of any plane graph with n vertices and maximum degree d on a (2n ? 5) (3 2 n ? 7 2) grid with at most 5n ? 15 bends and minimum angle > 2 d. In the constructed drawings, every edge has at most three bends and length O(n). To our best knowledge, this algorithm achieves the best simultaneous bounds concerning the gr...

With the rapid development of energy internet, dispatchers need to learn more knowledge with wider scope and fast update speed. It’s urgent realize electrification, systematization, visualization sharing power grid dispatching. Firstly, this paper studies definition traits graph, deeply analyses key technologies graph construction. Secondly, considering contents requirements dispatching busines...

Motivated by an application in image processing, we introduce the grid-leveling problem. It turns out to be the dual of a minimum cost flow problem for an apex graph with a grid graph as its basis. We present an O(n) algorithm for this problem. The optimum solution recovers missing DC coefficients from image and video coding by Discrete Cosine Transform used in popular standards like JPEG and M...

Abstract. This work describes properties of the mixed mesh approach that are especially suitable for generating families of meshes to assess the grid refinement convergence of CFD solvers. The paper outlines how a regular grid refinement is achieved throughout the domain. The distributions of characteristic grid quality metrics are compared and a grid convergence study is outlined for a commonl...

An exact formula is given for the maximum number of edges in a graph that admits a three-dimensional grid-drawing contained in a given bounding box. A three-dimensional (straight-line) grid-drawing of a graph represents the vertices by distinct points in Z, and represents each edge by a line-segment between its endpoints that does not intersect any other vertex, and does not intersect any other...

Golumbic, Lipshteyn and Stern proved that every graph can be represented as the edge intersection graph of paths on a grid, i.e., one can associate to each vertex of E-mail addresses: [email protected]; [email protected]; [email protected]; [email protected]; [email protected]; [email protected]; [email protected]. This work was partially supported by MathAmSud...

In this paper we extend the theory of bidimensionality to two families of graphs that do not exclude fixed minors: map graphs and power graphs. In both cases we prove a polynomial relation between the treewidth of a graph in the family and the size of the largest grid minor. These bounds improve the running times of a broad class of fixed-parameter algorithms. Our novel technique of using appro...

In this paper, we consider the problem of approximating the longest path in a grid graph that possesses a square-free 2-factor. By (1) analyzing several characteristics of four types of cross cells and (2) presenting three cycle-merging operations and one extension operation, we propose an algorithm that finds in an n-vertex grid graph G, a long path of length at least 6n + 2. Our approximation...

An r-dynamic k-coloring of a graph G is a proper k-coloring of G such that every vertex in V (G) has neighbors in at least min{d(v), r} different color classes. The rdynamic chromatic number of a graph G, written χr(G), is the least k such that G has such a coloring. Proving a conjecture of Jahanbekam, Kim, O, and West, we show that the m-by-n grid has no 3-dynamic 4-coloring whenmn ≡ 2 mod 4. ...