Fault Tolerance of Optical Hypercube Interconnection Networks with r -Communication Pattern

As power grids and optical interconnection networks are interdependent, the reliabilities of the optical networks are critical issues in power systems. The optical networks hold prominent performance including wide bandwidth, low loss, strong anti-interference capability, high fidelity, and reliable performance. They are regarded as promising alternatives to electrical networks for parallel processing. This paper is aimed at taking the first step in understanding the communication efficiencies of optical networks. For that purpose, on optical networks, we propose a series of novel notions including communication pattern, r -communication graph, reduced diameter, enhanced connectivity, r -diameter, and r -connectivity. Using these notions, we determine that the r -diameter and r -connectivity of the optical n -dimensional hypercube network are n / r and n 1 + n 2 + ⋯ + n r , respectively. Since the parameter r is variable, we can adjust different values of r on the basis of the wavelength resources and load of the optical networks, achieving enhanced communication efficiencies of these networks. Compared with the electric n -dimensional hypercube network, the proposed communication pattern on the optical hypercube network not only reduces the maximum communication delay of the conventional electrical hypercube significantly but also improves its fault tolerance remarkably.

Threshold Logic Technology based E-cube Routing on a 4-dimensional hypercube

Hypercube network connection is formed by connecting different N number of nodes that are expressed as a power of 2. If each node has an address of m bits then the total number of nodes in the Hypercube network is N=2^m. In calculating the predefined routing path for the case of this E-cube network, we apply deterministic algorithm which gives a deadlock free concept. For determining predefined routing path, node addresses involved in the path are calculated by using the exclusive operation, firstly, on the node addresses of source and destination, next, on the derived nodes according to the algorithm. In the present work, the Exclusive-OR operation is performed with the help of electron-tunneling based XOR gate which is made up of Multiple input threshold logic gate. This multiple input threshold logic gate technology is really different from the existing one. By using an emerging technology we are capable of making an electronic circuit with high speed, low cost, high concentration density, light in weight, reduced gate numbers and low power consumption. This technology is relies on the condition of linear threshold logic and electron-tunneling event. When we are interested in implementing a circuit, a multi-inputs but one-output based logic-gate will be taken account of consideration. In this work, we have designed an E-cube Routing on a 4-dimensional hypercube to find out the node addresses for predefining the deadlock free routing path from source to destination. To develop this “E-cube Routing on a 4-dimensional hypercube”, we must require a specific logic called Exclusive-OR gate and for this, some small components like 2-input OR gate, 2-input AND gates of different input conditions are essential. After arranging this XOR gate in a pattern discussed in section 2, a desired circuit is implemented. All the circuit we are intended to construct are given in due places with their threshold logic and simulation set, the simulation results are provided as well. Different truth tables, derivation of threshold logic expressions are given for clear understanding. We have taken our consideration of whether the present work circuits are faster or slower than the circuits of CMOS based- and Single electron transistor (SET) based-circuits. The power consumed at the time of tunneling event for a circuit is measured and sensed that it exists in the range between 10meV to 250meV which is very small amount. All the combinational circuits we have presented in this work are of ‘generic multiple input threshold logic gate’-based.

Performance Evaluation, Comparison and Identification of Efficient Hypercube Interconnection Networks

A Multiprocessor is a system with at least two processing units sharing access to memory. The principle goal of utilizing a multiprocessor is to process the undertakings all the while and support the system’s performance. An Interconnection Network interfaces the various handling units and enormously impacts the exhibition of the whole framework. Interconnection Networks, also known as Multi-stage Interconnection Networks, are node-to-node links in which each node may be a single processor or a group of processors. These links transfer information from one processor to the next or from the processor to the memory, allowing the task to be isolated and measured equally. Hypercube systems are a kind of system geography used to interconnect various processors with memory modules and precisely course the information. Hypercube systems comprise of 2n nodes. Any Hypercube can be thought of as a graph with nodes and edges, where a node represents a processing unit and an edge represents a connection between the processors to transmit. Degree, Speed, Node coverage, Connectivity, Diameter, Reliability, Packet loss, Network cost, and so on are some of the different system scales that can be used to measure the performance of Interconnection Networks. A portion of the variations of Hypercube Interconnection Networks include Hypercube Network, Folded Hypercube Network, Multiple Reduced Hypercube Network, Multiply Twisted Cube, Recursive Circulant, Exchanged Crossed Cube Network, Half Hypercube Network, and so forth. This work assesses the performing capability of different variations of Hypercube Interconnection Networks. A group of properties is recognized and a weight metric is structured utilizing the distinguished properties to assess the performance exhibition. Utilizing this weight metric, the performance of considered variations of Hypercube Interconnection Networks is evaluated and summed up to recognize the effective variant. A compact survey of a portion of the variations of Hypercube systems, geographies, execution measurements, and assessment of the presentation are examined in this paper. Degree and Diameter are considered to ascertain the Network cost. On the off chance that Network Cost is considered as the measurement to assess the exhibition, Multiple Reduced Hypercube stands ideal with its lower cost. Notwithstanding it, on the off chance that we think about some other properties/ scales/metrics to assess the performance, any variant other than MRH may show considerably more ideal execution. The considered properties probably won't be ideally adequate to assess the effective performance of Hypercube variations in all respects. On the off chance that a sensibly decent number of properties are utilized to assess the presentation, a proficient variation of Hypercube Interconnection Network can be distinguished for a wide scope of uses. This is the inspiration to do this research work.

On topological properties of hierarchical hypercube network based on Ve and Ev degree

Grid implementation is a principal unit in electrical and electronic engineering but it depends on the domain of these projects. For example, depending on the grid and the signal processing in that fields of electronic and electrical engineering, such as more abstract mathematics in signal conversion and e-transmission theory griding, etc. Provides transmission through grid nodes. Graph theory is very useful in research fields. As topological indices, there are more actual numbers associated with chemical composition complaints connected to the chemical grid with physical and chemical properties and reactions. In this paper, we expand the work to interconnected grid and examine the first Zagreb, the second Zagreb, Randic, sum-connectivity, harmonic, geometric, and atom bond connectivity exponents of hierarchical hypercube network based on vertex-edge and edge-vertex degree.

Upper and Lower Bounds for the Kirchhoff Index of the n-Dimensional Hypercube Network

The hypercube Qn is one of the most admirable and efficient interconnection network due to its excellent performance for some practical applications. The Kirchhoff index KfG is equal to the sum of resistance distances between any pairs of vertices in networks. In this paper, we deduce some bounds with respect to Kirchhoff index of hypercube network Qn.

Communication Performance Evaluation of the Locally Twisted Cube

The topology properties of multi-processors interconnection networks are important to the performance of high performance computers. The hypercube network [Formula: see text] has been proved to be one of the most popular interconnection networks. The [Formula: see text]-dimensional locally twisted cube [Formula: see text] is an important variant of [Formula: see text]. Fault diameter and wide diameter are two communication performance evaluation parameters of a network. Let [Formula: see text]), [Formula: see text] and [Formula: see text] denote the diameter, the [Formula: see text] fault diameter and the wide diameter of [Formula: see text], respectively. In this paper, we prove that [Formula: see text] if [Formula: see text] is an odd integer with [Formula: see text], [Formula: see text] if [Formula: see text] is an even integer with [Formula: see text].