|
Bisection Bandwidth
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. Bisection bandwidth calculations For a linear array with n nodes bisection bandwidth is one link bandwidth. For linear array only one link needs to be broken to bisect the network into two partitions. For ring topology with n nodes two links should be broken to bisect the network, so bisection bandwidth becomes bandwidth of two links. For tree topology with n nodes can be bisected at the root by breaking one link, so bisection bandwidth is one link ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bisection
In geometry, bisection is the division of something into two equal or congruent parts, usually by a line, which is then called a ''bisector''. The most often considered types of bisectors are the ''segment bisector'' (a line that passes through the midpoint of a given segment) and the ''angle bisector'' (a line that passes through the apex of an angle, that divides it into two equal angles). In three-dimensional space, bisection is usually done by a plane (geometry), plane, also called the ''bisector'' or ''bisecting plane''. Perpendicular line segment bisector Definition *The perpendicular bisector of a line segment is a line, which meets the segment at its midpoint perpendicularly. The Horizontal intersector of a segment AB also has the property that each of its points X is equidistant from the segment's endpoints: (D)\quad , XA, = , XB, . The proof follows from and Pythagoras' theorem: :, XA, ^2=, XM, ^2+, MA, ^2=, XM, ^2+, MB, ^2=, XB, ^2 \; . Property (D) is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Torus Interconnect
A torus interconnect is a switch-less network topology for connecting processing nodes in a parallel computer system. Introduction In geometry, a torus is created by revolving a circle about an axis coplanar to the circle. While this is a general definition in geometry, the topological properties of this type of shape describes the network topology in its essence. Geometry illustration The following images are 1D, and 2D torus. 1D torus is a simple circle, and 2D torus has the shape of a doughnut. The animation below illustrates how a 2D torus is generated from a rectangle by connecting its two pairs of opposite edges. Here the concept of torus is used to describe essentially the beginning and ending of a sequence of nodes are connected, like a doughnut. To better illustrate the concept, and understand what the topology means in network interconnect, we give 3 examples of parallel interconnected nodes using torus topology. At one dimension, a torus topology is equivalent to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bill Dally
William James Dally (born August 17, 1960) is an American computer scientist and educator. Since 2021, he has been a member of the President’s Council of Advisors on Science and Technology (PCAST). Microelectronics He developed a number of techniques used in modern interconnection networks including routing-based deadlock avoidance, wormhole routing, link-level retry, virtual channels, global adaptive routing, and high-radix routers. He has developed efficient mechanisms for communication, synchronization, and naming in parallel computers including message-driven computing and fast capability-based addressing. He has developed a number of stream processors starting in 1995 including Imagine, for graphics, signal, and Image processing, and Merrimac, for scientific computing. He has published over 200 papers as well as the textbooks "Digital Systems Engineering" with John Poulton, and "Principles and Practices of Interconnection Networks" with Brian Towles. He was inventor or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shuffle-exchange Network
In graph theory, the shuffle-exchange network is an undirected cubic multigraph, whose vertices represent binary sequences of a given length and whose edges represent two operations on these sequence, circular shifts and flipping the lowest-order bit. Definition In the version of this network introduced by Tomas Lang and Harold S. Stone in 1976, simplifying earlier work of Stone in 1971, the shuffle-exchange network of order d consisted of an array of 2^d cells, numbered by the 2^d different binary numbers that can be represented with d bits. These cells were connected by communications links in two different patterns: "exchange" links in which each cell is connected to the cell numbered with the opposite value in its lowest-order bit, and "shuffle" links in which each cell is connected to the cell whose number is obtained by a circular shift that shifts every bit to the next more significant position, except for the highest-order bit which shifts into the lowest-order position. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 discovered 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fast Fourier Transform
A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). Fourier analysis converts a signal from its original domain (often time or space) to a representation in the frequency domain and vice versa. The DFT is obtained by decomposing a sequence of values into components of different frequencies. This operation is useful in many fields, but computing it directly from the definition is often too slow to be practical. An FFT rapidly computes such transformations by factorizing the DFT matrix into a product of sparse (mostly zero) factors. As a result, it manages to reduce the complexity of computing the DFT from O\left(N^2\right), which arises if one simply applies the definition of DFT, to O(N \log N), where N is the data size. The difference in speed can be enormous, especially for long data sets where ''N'' may be in the thousands or millions. In the presence of round-off error, many FFT algorithm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hypercube Internetwork Topology
In computer networking, hypercube networks are a type of network topology used to connect multiple processors with memory modules and accurately route data. Hypercube networks consist of nodes, which 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 -ary -dimensional mesh topology family, where represents the number of dimensions and represents the number of nodes in each dimension. Topology Hypercube interconnection network is formed by connecting N nodes that can be expressed as a power of 2. This means if the network has N nodes it can be expressed as : N=2^m where m is the number of bits that are required to label the nodes in the network. So, if there are 4 nodes in the network, 2 bits are needed to represent all the nodes in the network. The network is constructed by connecting the nodes that just ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mesh Networking
A mesh network is a local area network topology in which the infrastructure nodes (i.e. bridges, switches, and other infrastructure devices) connect directly, dynamically and non-hierarchically to as many other nodes as possible and cooperate with one another to efficiently route data to and from clients. This lack of dependency on one node allows for every node to participate in the relay of information. Mesh networks dynamically self-organize and self-configure, which can reduce installation overhead. The ability to self-configure enables dynamic distribution of workloads, particularly in the event a few nodes should fail. This in turn contributes to fault-tolerance and reduced maintenance costs. Mesh topology may be contrasted with conventional star/tree local network topologies in which the bridges/switches are directly linked to only a small subset of other bridges/switches, and the links between these infrastructure neighbours are hierarchical. While star-and-tree topologi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Network Topology
Network topology is the arrangement of the elements ( links, 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 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 identical. A network’s physical topology is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
