In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices which are connected by edges. A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics.
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.
The fat tree network is a universal network for provably efficient communication. It was invented by Charles E. Leiserson of the Massachusetts Institute of Technology in 1985. k-ary n-trees, the type of fat-trees commonly used in most high-performance networks, were initially formalized in 1997.
In graph theory, a cut is a partition of the vertices of a graph into two disjoint subsets. Any cut determines a cut-set, the set of edges that have one endpoint in each subset of the partition. These edges are said to cross the cut. In a connected graph, each cut-set determines a unique cut, and in some cases cuts are identified with their cut-sets rather than with their vertex partitions.
TCP tuning techniques adjust the network congestion avoidance parameters of Transmission Control Protocol (TCP) connections over high-bandwidth, high-latency networks. Well-tuned networks can perform up to 10 times faster in some cases. However, blindly following instructions without understanding their real consequences can hurt performance as well.
In graph theory, a book embedding is a generalization of planar embedding of a graph to embeddings into a book, a collection of half-planes all having the same line as their boundary. Usually, the vertices of the graph are required to lie on this boundary line, called the spine, and the edges are required to stay within a single half-plane. The book thickness of a graph is the smallest possible number of half-planes for any book embedding of the graph. Book thickness is also called pagenumber, stacknumber or fixed outerthickness. Book embeddings have also been used to define several other graph invariants including the pagewidth and book crossing number.
A wireless ad hoc network (WANET) or mobile ad hoc network (MANET) is a decentralized type of wireless network. The network is ad hoc because it does not rely on a pre-existing infrastructure, such as routers or wireless access points. Instead, each node participates in routing by forwarding data for other nodes. The determination of which nodes forward data is made dynamically on the basis of network connectivity and the routing algorithm in use.
In mathematics, a graph partition is the reduction of a graph to a smaller graph by partitioning its set of nodes into mutually exclusive groups. Edges of the original graph that cross between the groups will produce edges in the partitioned graph. If the number of resulting edges is small compared to the original graph, then the partitioned graph may be better suited for analysis and problem-solving than the original. Finding a partition that simplifies graph analysis is a hard problem, but one that has applications to scientific computing, VLSI circuit design, and task scheduling in multiprocessor computers, among others. Recently, the graph partition problem has gained importance due to its application for clustering and detection of cliques in social, pathological and biological networks. For a survey on recent trends in computational methods and applications see Buluc et al. (2013). Two common examples of graph partitioning are minimum cut and maximum cut problems.
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; similarly to the mathematic concept of topology, 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.
For parallel computing, the interconnection network is the heart of a parallel processing system, and many systems have failed to meet their design goals for the design of their essential components. The bandwidth limitation of the electronic interconnects prompted the need for exploring alternatives that overcome this limitation. Optics is considered as an alternative that is capable of providing inherentcommunication, parallelism, high connectivity and large bandwidth. When the communication distances exceed a few millimeters, optical interconnects provide advantage over the electronic interconnects in term of power, speed and crosstalk property. Therefore, in the construction of very powerful and large multiprocessor systems, it is advantageous to interconnect close processors physically using electronic links and far processors using optical links. Thus we use optical network like OMTSE, OTIS, and OMULT etc. The OMTSE network consists of two different systems called as optical and electrical. In this network there are using two layer of TSE network with a complete binary trees of height one and the roots of these binary trees are connected with Shuffle-Exchange fashion.
A torus interconnect is a switch-less network topology for connecting processing nodes in a parallel computer system.
In computer networking, a flit is a link-level atomic piece that forms a network packet or stream. The first flit, called the header flit holds information about this packet's route and sets up the routing behavior for all subsequent flits associated with the packet. The header flit is followed by zero or more body flits, containing the actual payload of data. The final flit, called the tail flit, performs some book keeping to close the connection between the two nodes.
Data center is a pool of resources interconnected using a communication network. Data Center Network (DCN) holds a pivotal role in a data center, as it interconnects all of the data center resources together. DCNs need to be scalable and efficient to connect tens or even hundreds of thousands of servers to handle the growing demands of Cloud computing. Today's data centers are constrained by the interconnection network.
Approximate max-flow min-cut theorems are mathematical propositions in network flow theory. They deal with the relationship between maximum flow rate ("max-flow") and minimum cut ("min-cut") in a multi-commodity flow problem. The theorems have enabled the development of approximation algorithms for use in graph partition and related problems.
The STC104 switch, also known as the C104 switch in its early phases, is an asynchronous packet-routing chip that was designed for building high-performance point-to-point computer communication networks. It was developed by INMOS in the 1990s and was the first example of a general-purpose production packet routing chip. It was also the first routing chip to implement wormhole routing, to decouple packet size from the flow-control protocol, and to implement interval and two-phase randomized routing.
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:
A Wireless Data center is a type of data center that uses wireless communication technology instead of cables to store, process and retrieve data for enterprises. The development of Wireless Data centers arose as a solution to growing cabling complexity and hotspots. The wireless technology was introduced by Shin et al., who replaced all cables with 60 GHz wireless connections at the Cayley data center.
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.
