Numerical methods for the solution of partial di↵erential equations constitute an important class of techniques in scientific computing. Often, the discretization is based on approximating the partial derivatives by finite di↵erences on a regular Cartesian grid. The resulting computations are structured in the sense of updating a large, multidimensional array by a stencil operation. A stencil d...

We show that if a very large grid is embedded in a surface, then a large subgrid is embedded in a disc in the surface. This readily implies that: (a) a minor-minimal graph that does not embed in a given surface has no very large grid; and (b) a minor-minimal k-representative embedding in the surface has no very large grid. Similar arguments show (c) that if G is minimal with respect to crossing...

We consider the problem of simultaneous embedding of planar graphs. There are two variants of this problem, one in which the mapping between the vertices of the two graphs is given and another where the mapping is not given. In particular, we show that without mapping, any number of outerplanar graphs can be embedded simultaneously on an O(n)×O(n) grid, and an outerplanar and general planar gra...

We introduce the concept of multi-directional width-bounded geometric separators and obtain an improved separator for grid graphs. This yields an improved exact algorithm for the protein folding problem in the HP-model. For a grid graph G with n grid points P , there exists a separator A ⊆ P such that A has at most 1.02074 √ n points, and G−A has two disconnected subgraphs each with at most 2 3...

A straight-line grid drawing of a plane graph G is a planar drawing of G, where each vertex is drawn at a grid point of an integer grid and each edge is drawn as a straight-line segment. The area of such a drawing is the area of the smallest axis-aligned rectangle on the grid which encloses the drawing. A minimum-area drawing of a plane graph G is a straight-line grid drawing of G where the are...

Grid workflow and its application are one of main focuses of Grid Computing. Due to data or control dependencies between tasks and the requirement of no directed circuit, Directed Acyclic Graph (DAG) is a natural model for Grid workflow, and has been extensively used in Grid workflow modeling. For some workflow applications, there may exist another requirement that each task should be accomplis...

“Eventization” of power grid monitoring is an effective way to deal with massive alarm information. The existing event recognition method adopts the text information mining, and overall accuracy not high. Therefore, this paper proposes a integrating knowledge graph deep learning. First, constructs equipment uses improved GraphSAGE (graph sample aggregate) algorithm perform representation learni...

Abstract Let G and H be two simple undirected graphs An embedding of the graph G into the graph H is an injective mapping f from the vertices of G to the vertices of H together with a mapping which assigns to each edge u v of G a path between f u and f v in H The grid M r s is the graph whose vertex set is the set of pairs on nonnegative integers f i j i r j sg in which there is an edge between...

This paper describes a generalized sequential diagnosis algorithm whose analysis leads to strong diagnosability results for a variety of multiprocessor interconnection topologies. The overall complexity of this algorithm in terms of total testing and syndrome decoding time is linear in the number of edges in the interconnection graph and the total number of iterations of diagnosis and repair ne...

QoS-Based Services Selecting and Optimizing Composition between the peers play an increasingly important role to ensure interoperability on Grid environment. However, the prohibitive cost of selecting, matching, mapping and composing algorithm has now become a key bottleneck hindering the deployment of a wide variety of Grid services. In this paper, we present QoS-Based Services Selecting and O...