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Grid Network
A grid network is a computer network consisting of a number of computer systems connected in a grid topology. 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. A parallel computing cluster or multi-core processor is often connected in regular interconnection network such as a de Bruijn graph,
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Hypercube Graph
In graph theory, the hypercube graph is the graph formed from the vertices and edges of an -dimensional hypercube. For instance, the cubical graph, cube graph is the graph formed by the 8 vertices and 12 edges of a three-dimensional cube. has vertex (graph theory), vertices, edges, and is a regular graph with edges touching each vertex. The hypercube graph may also be constructed by creating a vertex for each subset of an -element set, with two vertices adjacent when their subsets differ in a single element, or by creating a vertex for each -digit binary number, with two vertices adjacent when their binary representations differ in a single digit. It is the -fold Cartesian product of graphs, Cartesian product of the two-vertex complete graph, and may be decomposed into two copies of connected to each other by a perfect matching. Hypercube graphs should not be confused with cubic graphs, which are graphs that have exactly three edges touching each vertex. The only hyperc ...
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Network Topology
Network topology is the arrangement of the elements (Data link, links, Node (networking), nodes, etc.) 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 Fieldbus, fieldbusses and computer networks. Network topology is the topological structure of a network and may be depicted physically or logically. It is an application of graph theory wherein communicating devices are modeled as nodes and the connections between the devices are modeled as links or lines between the nodes. Physical topology is the placement of the various components of a network (e.g., device location and cable installation), while logical topology illustrates how data flows within a network. Distances between nodes, physical interconnections, transmission rates, or signal types may differ between two different networks, yet their logical topologies may be identica ...
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Grid Plan
In urban planning, the grid plan, grid street plan, or gridiron plan is a type of city plan in which streets run at right angles to each other, forming a grid. Two inherent characteristics of the grid plan, frequent intersections and orthogonal geometry, facilitate movement. The geometry helps with orientation and wayfinding and its frequent intersections with the choice and directness of route to desired destinations. In ancient Rome, the grid plan method of land measurement was called centuriation. The grid plan dates from antiquity and originated in multiple cultures; some of the earliest planned cities were built using grid plans in the Indian subcontinent. History Ancient grid plans By 2600 BC, Mohenjo-daro and Harappa, major cities of the Indus Valley civilization, were built with blocks divided by a grid of straight streets, running north–south and east–west. Each block was subdivided by small lanes. The cities and monasteries of Sirkap, Taxila and Thimi (in ...
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Grid Computing
Grid computing is the use of widely distributed computer resources to reach a common goal. A computing grid can be thought of as a distributed system with non-interactive workloads that involve many 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 (thus not physically coupled) 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. Grids are a form of distributed computing composed of many networked loosely coupled computers acting together to perform large tasks. For certain applications, distributed or grid computing can be seen as a special ...
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Computational Grid
Grid computing is the use of widely distributed computer resources to reach a common goal. A computing grid can be thought of as a distributed system with non-interactive workloads that involve many 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 (thus not physically coupled) 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. Grids are a form of distributed computing composed of many networked loosely coupled computers acting together to perform large tasks. For certain applications, distributed or grid computing can be seen as a special type of ...
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Cube-connected Cycles
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 for use as a network topology in parallel computing. Definition The cube-connected cycles of order ''n'' (denoted CCC''n'') can be defined as a graph formed from a set of ''n''2''n'' nodes, indexed by pairs of numbers (''x'', ''y'') where 0 ≤ ''x'' < 2''n'' and 0 ≤ ''y'' < ''n''. Each such node is connected to three neighbors: , , and , where "⊕" denotes the bitwise exclusive or operation on binary numbers. This graph can also be interpreted as the result of replacing each vertex of an ''n''-dimensional hypercube graph by an ''n''-vertex cycle. The hypercube graph vertices are indexed by the numbers ''x'', and the positions within each cycle by the numbers ''y''. Properties The cube-connected cycles of order ''n'' is the Cayley graph of a group that acts on binary words of length ''n'' by rotation an ...
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Fat Tree
The fat tree network is a universal network for provably efficient communication. It was invented by Charles E. Leiserson of the MIT in 1985. k-ary n-trees, the type of fat-trees commonly used in most high-performance networks, were initially formalized in 1997. In a tree data structure, every branch has the same thickness (bandwidth), regardless of their place in the hierarchy—they are all "skinny" (''skinny'' in this context means low-bandwidth). In a fat tree, branches nearer the top of the hierarchy are "fatter" (thicker) than branches further down the hierarchy. In a telecommunications network, the branches are data links; the varied thickness (bandwidth) of the data links allows for more efficient and technology-specific use. Mesh and hypercube topologies have communication requirements that follow a rigid algorithm, and cannot be tailored to specific packaging technologies. Applications in supercomputers Supercomputers that use a fat tree network include the two fast ...
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Hypertree Network
A hypertree network is a network topology that shares some traits with the binary tree network. It is a variation of the fat tree architecture. A hypertree of degree ''k'' depth ''d'' may be visualized as a 3-dimensional object whose front view is the top-down complete k-ary tree of depth ''d'' and the side view is the bottom-up complete binary tree of depth ''d''. Hypertrees were proposed in 1981 by James R. Goodman and Carlo Sequin. Hypertrees are a choice for parallel computer architecture, used, e.g., in the connection machine The Connection Machine (CM) is a member of a series of massively parallel supercomputers sold by Thinking Machines Corporation. The idea for the Connection Machine grew out of doctoral research on alternatives to the traditional von Neumann arch ... CM-5. References Network topology {{Compu-network-stub ...
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De Bruijn Graph
In graph theory, an -dimensional De Bruijn graph of symbols is a directed graph representing overlaps between sequences of symbols. It has vertices, consisting of all possible sequences of the given symbols; the same symbol may appear multiple times in a sequence. For a set of symbols the set of vertices is: :V=S^n=\. If one of the vertices can be expressed as another vertex by shifting all its symbols by one place to the left and adding a new symbol at the end of this vertex, then the latter has a directed edge to the former vertex. Thus the set of arcs (that is, directed edges) is :E=\. Although De Bruijn graphs are named after Nicolaas Govert de Bruijn, they were invented independently by both de Bruijn and I. J. Good. Much earlier, Camille Flye Sainte-Marie implicitly used their properties. Properties * If , then the condition for any two vertices forming an edge holds vacuously, and hence all the vertices are connected, forming a total of edges. * Each vertex has e ...
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Computer Network
A computer network is a collection of communicating computers and other devices, such as printers and smart phones. In order to communicate, the computers and devices must be connected by wired media like copper cables, optical fibers, or by wireless communication. The devices may be connected in a variety of network topologies. In order to communicate over the network, computers use agreed-on rules, called communication protocols, over whatever medium is used. The computer network can include personal computers, Server (computing), servers, networking hardware, or other specialized or general-purpose Host (network), hosts. They are identified by network addresses and may have hostnames. Hostnames serve as memorable labels for the nodes and are rarely changed after initial assignment. Network addresses serve for locating and identifying the nodes by communication protocols such as the Internet Protocol. Computer networks may be classified by many criteria, including the tr ...
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Multi-core
A multi-core processor (MCP) is a microprocessor on a single integrated circuit (IC) with two or more separate central processing units (CPUs), called ''cores'' to emphasize their multiplicity (for example, ''dual-core'' or ''quad-core''). Each core reads and executes program instructions, specifically ordinary CPU instructions (such as add, move data, and branch). However, the MCP can run instructions on separate cores at the same time, increasing overall speed for programs that support multithreading or other parallel computing techniques. Manufacturers typically integrate the cores onto a single IC die, known as a ''chip multiprocessor'' (CMP), or onto multiple dies in a single chip package. As of 2024, the microprocessors used in almost all new personal computers are multi-core. A multi-core processor implements multiprocessing in a single physical package. Designers may couple cores in a multi-core device tightly or loosely. For example, cores may or may not share c ...
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