# Grid network

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A grid network is a computer network consisting of a number of (computer) systems connected in a grid topology. A computer network is a digital telecommunications network which allows nodes to share resources. In computer networks, computing devices exchange data with each other using connections between nodes. These data links are established over cable media such as wires or optic cables, or wireless media such as Wi-Fi.

In a regular grid topology, each node in the network is connected with two neighbors along one or more dimensions. If the network is one-dimensional, and the chain of nodes is connected to form a circular loop, the resulting topology is known as a ring. Network systems such as FDDI use two counter-rotating token-passing rings to achieve high reliability and performance. In general, when an n-dimensional grid network is connected circularly in more than one dimension, the resulting network topology is a torus, and the network is called "toroidal". When the number of nodes along each dimension of a toroidal network is 2, the resulting network is called a hypercube. In physics and mathematics, the dimension of a mathematical space is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it – for example, the point at 5 on a number line. A surface such as a plane or the surface of a cylinder or sphere has a dimension of two because two coordinates are needed to specify a point on it – for example, both a latitude and longitude are required to locate a point on the surface of a sphere. The inside of a cube, a cylinder or a sphere is three-dimensional because three coordinates are needed to locate a point within these spaces. In geometry, a torus is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle. If the axis of revolution does not touch the circle, the surface has a ring shape and is called a torus of revolution. In geometry, a hypercube is an n-dimensional analogue of a square and a cube. It is a closed, compact, convex figure whose 1-skeleton consists of groups of opposite parallel line segments aligned in each of the space's dimensions, perpendicular to each other and of the same length. A unit hypercube's longest diagonal in n dimensions is equal to .

A parallel computing cluster or multi-core processor is often connected in regular interconnection network such as a de Bruijn graph,  a hypercube graph, a hypertree network, a fat tree network, a torus, or cube-connected cycles. Parallel computing is a type of computation in which many calculations or the execution of processes are carried out simultaneously. Large problems can often be divided into smaller ones, which can then be solved at the same time. There are several different forms of parallel computing: bit-level, instruction-level, data, and task parallelism. Parallelism has long been employed in high-performance computing, but it's gaining broader interest due to the physical constraints preventing frequency scaling. As power consumption by computers has become a concern in recent years, parallel computing has become the dominant paradigm in computer architecture, mainly in the form of multi-core processors.

In graph theory, an n-dimensional De Bruijn graph of m symbols is a directed graph representing overlaps between sequences of symbols. It has mn vertices, consisting of all possible length-n sequences of the given symbols; the same symbol may appear multiple times in a sequence. If we have the set of m symbols then the set of vertices is: In graph theory, the hypercube graphQn is the graph formed from the vertices and edges of an n-dimensional hypercube. For instance, the cubical graph Q3 is the graph formed by the 8 vertices and 12 edges of a three-dimensional cube. Qn has 2n vertices, 2n−1n edges, and is a regular graph with n edges touching each vertex.

Note that a grid network is not the same as a grid computer (or computational grid) (even though the nodes in a grid network are usually computers, and grid computing obviously requires some kind of computer network or "universal coding" to interconnect the computers).

Grid computing is the use of widely distributed computer resources to reach a common goal. The grid can be thought of as a distributed system with non-interactive workloads that involve a large number of files. Grid computing is distinguished from conventional high-performance computing systems such as cluster computing in that grid computers have each node set to perform a different task/application. Grid computers also tend to be more heterogeneous and geographically dispersed than cluster computers. Although a single grid can be dedicated to a particular application, commonly a grid is used for a variety of purposes. Grids are often constructed with general-purpose grid middleware software libraries. Grid sizes can be quite large.

## Related Research Articles

Distributed computing is a field of computer science that studies distributed systems. A distributed system is a system whose components are located on different networked computers, which communicate and coordinate their actions by passing messages to one another. The components interact with one another in order to achieve a common goal. Three significant characteristics of distributed systems are: concurrency of components, lack of a global clock, and independent failure of components. Examples of distributed systems vary from SOA-based systems to massively multiplayer online games to peer-to-peer applications. A star network is an implementation of a spoke–hub distribution paradigm in computer networks. In a star network, every host is connected to a central hub. In its simplest form, one central hub acts as a conduit to transmit messages. The star network is one of the most common computer network topologies. Network topology is the arrangement of the elements of a communication network. Network topology can be used to define or describe the arrangement of various types of telecommunication networks, including command and control radio networks, industrial fieldbusses, and computer networks. In the mathematical field of graph theory, a complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique edge. A complete digraph is a directed graph in which every pair of distinct vertices is connected by a pair of unique edges. In computing, MIMD is a technique employed to achieve parallelism. Machines using MIMD have a number of processors that function asynchronously and independently. At any time, different processors may be executing different instructions on different pieces of data. MIMD architectures may be used in a number of application areas such as computer-aided design/computer-aided manufacturing, simulation, modeling, and as communication switches. MIMD machines can be of either shared memory or distributed memory categories. These classifications are based on how MIMD processors access memory. Shared memory machines may be of the bus-based, extended, or hierarchical type. Distributed memory machines may have hypercube or mesh interconnection schemes.

Toroidal describes something which resembles or relates to a torus or toroid:

In computer networking, if the network is bisected into two partitions, the bisection bandwidth of a network topology is the bandwidth available between the two partitions. Bisection should be done in such a way that the bandwidth between two partitions is minimum. Bisection bandwidth gives the true bandwidth available in the entire system. Bisection bandwidth accounts for the bottleneck bandwidth of the entire network. Therefore bisection bandwidth represents bandwidth characteristics of the network better than any other metric.

In distributed computing, leader election is the process of designating a single process as the organizer of some task distributed among several computers (nodes). Before the task is begun, all network nodes are either unaware which node will serve as the "leader" of the task, or unable to communicate with the current coordinator. After a leader election algorithm has been run, however, each node throughout the network recognizes a particular, unique node as the task leader. In graph theory, the cube-connected cycles is an undirected cubic graph, formed by replacing each vertex of a hypercube graph by a cycle. It was introduced by Preparata & Vuillemin (1981) for use as a network topology in parallel computing.

In peer-to-peer networks, Koorde is a Distributed hash table (DHT) system based on the Chord DHT and the De Bruijn graph. Inheriting the simplicity of Chord, Koorde meets O(log n) hops per node, and O(log n/ log log n) hops per lookup request with O(log n) neighbors per node. In mathematics, a toroid is a surface of revolution with a hole in the middle, like a doughnut, forming a solid body. The axis of revolution passes through the hole and so does not intersect the surface. For example, when a rectangle is rotated around an axis parallel to one of its edges, then a hollow rectangle-section ring is produced. If the revolved figure is a circle, then the object is called a torus.

The QCDOC is a supercomputer technology focusing on using relatively cheap low power processing elements to produce a massively parallel machine. The machine is custom-made to solve small but extremely demanding problems in the fields of quantum physics.

Multistage interconnection networks (MINs) are a class of high-speed computer networks usually composed of processing elements (PEs) on one end of the network and memory elements (MEs) on the other end, connected by switching elements (SEs). The switching elements themselves are usually connected to each other in stages, hence the name.

The topology of an electronic circuit is the form taken by the network of interconnections of the circuit components. Different specific values or ratings of the components are regarded as being the same topology. Topology is not concerned with the physical layout of components in a circuit, nor with their positions on a circuit diagram. It is only concerned with what connections exist between the components. There may be numerous physical layouts and circuit diagrams that all amount to the same topology. A torus interconnect is a switch-less network topology for connecting processing nodes in a parallel computer system. Hypercube networks are a type of network topology used to connect multiple processors with memory modules and accurately route data. Hypercube networks consist of 2m nodes. These nodes form the vertices of squares to create an internetwork connection. A hypercube is basically a multidimensional mesh network with two nodes in each dimension. Due to similarity, such topologies are usually grouped into a k-ary d-dimensional mesh topology family where d represents the number of dimensions and k represents the number of nodes in each dimension. A butterfly network is a technique to link multiple computers into a high-speed network. This form of multistage interconnection network topology can be used to connect different nodes in a multiprocessor system. The interconnect network for a shared memory multiprocessor system must have low latency and high bandwidth unlike other network systems, like local area networks (LANs) or internet for three reasons:

1. "A Network-based Asynchronous Architecture for Cryptographic Devices" by Ljiljana Spadavecchia 2005. section "5.6.1.2 De Bruijn graphs", and section "5.6.2.2 Randomised routing in de Bruijn graphs".