Abstract The stability and high quality of electricity are the basic factors which ensure that residents enterprises lead a happy productive life. Therefore, in order to meet requirements residents’ life enterprise production, it is necessary improve efficiency accuracy power grid fault diagnosis. In this paper, knowledge graph integrated into diagnosis, diagnosis system constructed realise gri...

A three-dimensional grid drawing of a graph is a placement of the vertices at distinct points with integer coordinates, such that the straight line segments representing the edges do not cross. Our aim is to produce three-dimensional grid drawings with small bounding box volume. Our first main result is that every nvertex graph with bounded degeneracy has a three-dimensional grid drawing with O...

Every planar graph has a crossings-free drawing in the plane. Formally, a straight-line drawing of a planar graph G is one where each vertex is placed at a point in the plane and each edge is represented by a straight-line segment between the two corresponding points such that no two edges cross each other, except possibly at their common endpoints. A straight-line grid drawing of G is a straig...

This study aims to increase the productivity of grid systems by an improved scheduling method. A brief overview and analysis of the main scheduling methods in grid systems are presented. A method for increasing efficiency by optimizing the task graph structure considering the grid system node structure is proposed. Task granularity (the ratio between the amount of computation and transferred da...

A key theorem in algorithmic graph-minor theory is a min-max relation between the treewidth of a graph and its largest grid minor. This min-max relation is a keystone of the Graph Minor Theory of Robertson and Seymour, which ultimately proves Wagner’s Conjecture about the structure of minor-closed graph properties. In 2008, Demaine and Hajiaghayi proved a remarkable linear min-max relation for ...

The bisection problem asks for a partition of the n vertices of a graph into two sets of size at most dn/2e, so that the number of edges connecting the two sets is minimised. A grid graph is a finite connected subgraph of the infinite two-dimensional grid. It is called solid if it has no holes. Papadimitriou and Sideri [7] gave an O(n) time algorithm to solve the bisection problem on solid grid...

A straight line grid embedding of a plane graph G is a drawing of G such that the vertices are drawn at grid points and the edges are drawn as non-intersecting straight line segments. In this paper, we show that, if an internally triangulated plane graph G has no non-empty triangles (a non-empty triangle is a triangle of G containing some vertices in its interior), then G can be embedded on a g...

A supergrid graph is a finite induced subgraph of the infinite graph associated with the two-dimensional supergrid. The supergrid graphs contain grid graphs and triangular grid graphs as subgraphs. The Hamiltonian cycle problem for grid and triangular grid graphs was known to be NP-complete. In the past, we have shown that the Hamiltonian cycle problem for supergrid graphs is also NP-complete. ...

Let γm,n denote the size of a minimum dominating set in the m× n grid graph. For the square grid graph, exact values for γn,n have earlier been published for n 6 19. By using a dynamic programming algorithm, the values of γm,n for m,n 6 29 are here obtained. Minimum dominating sets for square grid graphs up to size 29× 29 are depicted. ∗Supported by the Academy of Finland, Grant No. 132122 and ...