In this paper we extend general grid graphs to the grid graphs consist of polygons tiling on a plane, named polygonal grid graphs. With a cycle basis satisfied polygons tiling, we study the cyclic structure of Hamilton graphs. A Hamilton cycle can be expressed as a symmetric difference of a subset of cycles in the basis. From the combinatorial relations of vertices in the subset of cycles in th...

A disk graph is the intersection graph of disks in the plane, a unit disk graph is the intersection graph of same radius disks in the plane, and a segment graph is an intersection graph of line segments in the plane. Every disk graph can be realized by disks with centers on the integer grid and with integer radii; and similarly every unit disk graph can be realized by disks with centers on the ...

Given sensor readings over time from a power grid, how can we accurately detect when an anomaly occurs? A key part of achieving this goal is to use the network grid sensors quickly detect, in real-time, any unusual events, whether natural faults or malicious, occur on grid. Existing bad-data detectors industry lack sophistication robustly broad types anomalies, especially those due emerging cyb...

Replica placement is one of the important factors to improve performance in data grid systems. A good replica placement algorithm can result in good performance gains. It should be mentioned that, these algorithms or strategies are dependent on architecture of the data grid. By considering different kinds of architecture in data grid systems, a true representation of a grid is a general graph. ...

Smart grid envisions the potential to manage diverse energy resources and enable a future self-dispatch and selfhealing grid. This would first require the micro-grid visibility of node behavior (i.e. electrical parameters). In this paper we propose a novel approach to construct a stochastic model that makes global inference on every node at the micro-grid level. The micro-grid system can be mod...

Let G = (V,E) be a graph. All graphs considered are simple, £nite and undirected. A grid drawing of G is an injective mapping θ : V → Z such that for all edges vw ∈ E and vertices x ∈ V , θ(x) ∈ θ(v)θ(w) implies that x = v or x = w, where ab denotes the line-segment with endpoints a and b. That is, a grid drawing of a graph represents each vertex by a distinct gridpoint in the plane, and each e...

We look at a variant of the Hamilton circuit problem, where the input is restricted to hexagonal grid graphs. A hexagonal grid graph has a vertex set that is a subset of the grid points of a regular hexagonal tiling of the plane and edges corresponding to hexagon sides. We show that Hamilton circuit in hexagonal grid graphs is NP-complete.