Design of Fault Tolerant Shuffle Exchange Gamma Interconnection Network Layouts

2017 ◽  
Vol 17 (02) ◽  
pp. 1750005 ◽  
Author(s):  
GAURAV KHANNA ◽  
RAJESH MISHRA ◽  
S. K. CHATURVEDI
Keyword(s):  
Interconnection Networks ◽  
Fault Tolerant ◽  
Interconnection Network ◽  
Cost Effective ◽  
Disjoint Paths ◽  
Multiple Processors ◽  
Memory Modules ◽  
Telephone Industry ◽  
Exchange Network ◽  
Shuffle Exchange Network

Advancement in technology has resulted in increased computing power with the use of multiple processors within a system. These multiple processors need to communicate with each other and with memory modules. Multistage Interconnection Networks (MINs) provide a communication medium in such multi-processor systems by interconnecting a number of processors and memory modules. Besides, MINs also provide a cost effective substitute to costly crossbars in parallel computers and switching systems in telephone industry. This paper introduces two new fault-tolerant MINs named as Shuffle Exchange Gamma Interconnection Networks (SEGIN-1 and SEGIN-2). SEGIN-1 and SEGIN-2 can be obtained by altering Shuffle Exchange Network with one extra stage (SEN+) and provide two disjoint paths similar to it. Performance of SEGIN-1 and SEGIN-2 has been evaluated in terms of alternative paths, disjoint paths, reliability and hardware cost, and is compared with some very famous MINs like Shuffle Exchange Network (SEN), Shuffle Exchange Network with one extra stage (SEN+), Shuffle Exchange Network with two extra stage (SEN+2), Extra Stage Cube (ESC) and Gamma Interconnection Network (GIN). Results suggest that SEGINs surpass all the compared networks; hence, the proposed designs seem to be suitable for implementing practical interconnection networks.

A New SEN Minus: Design and Reliability Measures

2016 ◽  
Vol 23 (04) ◽  
pp. 1650012 ◽  
Author(s):  
Shilpa Gupta ◽  
G. L. Pahuja
Keyword(s):  
Interconnection Networks ◽  
Fault Tolerant ◽  
Network Size ◽  
Specific Class ◽  
Multistage Interconnection Networks ◽  
Multiprocessing Systems ◽  
Reliability Performance ◽  
Exchange Network ◽  
Partial Connectivity ◽  
Shuffle Exchange Network

Multistage interconnection networks (MIN) are becoming attractive choice as they provide fast and efficient communication at reasonable cost, for multiprocessing systems. Shuffle exchange network (SEN) are specific class of MIN characterized as lowest cost unipath MIN. Several developments have made SEN MIN fault tolerant with redundant paths by increasing the number or size of switching elements (SE). However, recently [Formula: see text] has been advanced by reducing the number of stages, but has serious limitation namely: (i) partial connectivity of each source–destination pair, (ii) unique path. A new method has been proposed in this paper to develop a new topology of MIN with one stage less than the basic unipath MIN of same class with multiple and disjoint path facility that mitigates the shortcomings of the above network and is truly [Formula: see text] MIN. Due to less number of stages used in the proposed network communication delays are also reduced as the path length is reduced. Parametric performances such as Terminal, Broadcast and Network Reliabilities, MTTF, Bandwidth have been computed for different network sizes and demonstrated that it not only outperforms other SEN variants, but has improved features of fault tolerance all because of disjoint minimal path set. Further the comments generated previously in literature about better reliability performance of [Formula: see text] than other two networks [Formula: see text] have been refuted and have demonstrated that [Formula: see text]2 network has better performance than other two for larger network size. Also it can be concluded that the performance of proposed [Formula: see text] is best among all these networks.

Fault-Tolerant Maximal Local-Connectivity on Cayley Graphs Generated by Transpositions

2019 ◽  
Vol 30 (08) ◽  
pp. 1301-1315 ◽  
Author(s):  
Liqiong Xu ◽  
Shuming Zhou ◽  
Weihua Yang
Keyword(s):  
Fault Tolerance ◽  
Interconnection Networks ◽  
Fault Tolerant ◽  
Interconnection Network ◽  
Cayley Graphs ◽  
Disjoint Paths ◽  
Local Connectivity ◽  
Communication Links ◽  
Restricted Condition ◽  
Vertex Disjoint

An interconnection network is usually modeled as a graph, in which vertices and edges correspond to processors and communication links, respectively. Connectivity is an important metric for fault tolerance of interconnection networks. A graph [Formula: see text] is said to be maximally local-connected if each pair of vertices [Formula: see text] and [Formula: see text] are connected by [Formula: see text] vertex-disjoint paths. In this paper, we show that Cayley graphs generated by [Formula: see text]([Formula: see text]) transpositions are [Formula: see text]-fault-tolerant maximally local-connected and are also [Formula: see text]-fault-tolerant one-to-many maximally local-connected if their corresponding transposition generating graphs have a triangle, [Formula: see text]-fault-tolerant one-to-many maximally local-connected if their corresponding transposition generating graphs have no triangles. Furthermore, under the restricted condition that each vertex has at least two fault-free adjacent vertices, Cayley graphs generated by [Formula: see text]([Formula: see text]) transpositions are [Formula: see text]-fault-tolerant maximally local-connected if their corresponding transposition generating graphs have no triangles.

TERMINAL RELIABILITY IMPROVEMENT OF SHUFFLE-EXCHANGE NETWORK SYSTEMS

2005 ◽  
Vol 12 (01) ◽  
pp. 51-60 ◽  
Author(s):  
NASSER S. FARD ◽  
INDRA GUNAWAN
Keyword(s):  
Interconnection Networks ◽  
Reliability Evaluation ◽  
Network Systems ◽  
Output Terminal ◽  
Memory Modules ◽  
Input Source ◽  
Efficient Information ◽  
Terminal Reliability ◽  
Exchange Network ◽  
Shuffle Exchange Network

Multistage Interconnection Networks (MINs) are communication network systems that provide fast and efficient information transitions among N processors and N memory modules of systems. A typical MIN consists of layers of switching elements that are connected together in a predefined topology. The routing capability of a network depends on its specific topology. A shuffle-exchange network (SEN), a specific type of MIN that consists of 2 × 2 switching elements, has been widely considered a practical interconnection system. In this paper, a modified shuffle-exchange network with 1 × 2 switching elements at the input (source) stage, 2 × 2 switching elements at the intermediate stages, and 2 × 1 switching elements at the output (terminal) stage is proposed. The proposed network shows an improvement in the terminal reliability of SEN. The terminal reliability evaluation of the SEN and the modified SEN are demonstrated through numerical examples for different sizes of networks. The reliability evaluation of MINs is important, as it determines the usability and efficiency of the network to provide services. It is shown that the proposed modified SEN provides higher terminal reliability for network sizes larger than 4 inputs and 4 outputs (4 × 4).

SEGIN-Minus: A New Approach to Design Reliable and Fault-Tolerant MIN

2020 ◽  
Vol 13 (3) ◽  
pp. 370-380
Author(s):  
Shilpa Gupta ◽  
Gobind Lal Pahuja
Keyword(s):  
Fault Tolerance ◽  
Interconnection Networks ◽  
Fault Tolerant ◽  
Interconnection Network ◽  
Network Reliability ◽  
Low Cost ◽  
Destination Node ◽  
Node Pair ◽  
Output Terminal ◽  
Multiple Processors

Background: VLSI technology advancements have resulted the requirements of high computational power, which can be achieved by implementing multiple processors in parallel. These multiple processors have to communicate with their memory modules by using Interconnection Networks (IN). Multistage Interconnection Networks (MIN) are used as IN, as they provide efficient computing with low cost. Objective: the objective of the study is to introduce new reliable MIN named as a (Shuffle Exchange Gamma Interconnection Network Minus) SEGIN-Minus, which provide reliability and faulttolerance with less number of stages. Methods: MUX at input terminal and DEMUX at output terminal of SEGIN has been employed with reduction in one intermidiate stage. Fault tolerance has been introduced in the form of disjoint paths formed between each source-destnation node pair. Hence reliability has been improved. Results: Terminal, Broadcast and Network Reliability has been evaluated by using Reliability Block Diagrams for each source-destination node pair. The results have been shown, which depicts the hiher reliability values for newly proposed network. The cost analysis shows that new SEGINMinus is a cheaper network than SEGIN. Conclusion: SEGIN-Minus has better reliability and Fault-tolerance than priviously proposed SEGIN.

Fault-Tolerant Maximal Local-Edge-Connectivity of Augmented Cubes

2020 ◽  
Vol 30 (03) ◽  
pp. 2040001
Author(s):  
Liyang Zhai ◽  
Liqiong Xu ◽  
Weihua Yang
Keyword(s):  
Regular Graph ◽  
Interconnection Networks ◽  
Fault Tolerant ◽  
Interconnection Network ◽  
Disjoint Paths ◽  
Communication Links ◽  
Restricted Condition ◽  
Local Edge ◽  
Augmented Cube ◽  
Cube Formula

An interconnection network is usually modeled as a graph, in which vertices and edges correspond to processors and communication links, respectively. Connectivity is an important metric for fault tolerance of interconnection networks. A connected graph [Formula: see text] is said to be maximally local-edge-connected if each pair of vertices [Formula: see text] and [Formula: see text] of [Formula: see text] are connected by [Formula: see text] pairwise edge-disjoint paths. In this paper, we show that the [Formula: see text]-dimensional augmented cube [Formula: see text] is [Formula: see text]-edge-fault-tolerant maximally local-edge-connected and the bound [Formula: see text] is sharp; under the restricted condition that each vertex has at least three fault-free adjacent vertices, [Formula: see text] is [Formula: see text]-edge-fault-tolerant maximally local-edge-connected and the bound [Formula: see text] is sharp; and under the restricted condition that each vertex has at least [Formula: see text] fault-free adjacent vertices, [Formula: see text] is [Formula: see text]-edge-fault-tolerant maximally local-edge-connected. Furthermore, we show that a [Formula: see text]-regular graph [Formula: see text] is [Formula: see text]-fault-tolerant one-to-many maximally local-connected if [Formula: see text] does not contain [Formula: see text] and is super [Formula: see text]-vertex-connected of order 1, a [Formula: see text]-regular graph [Formula: see text] is [Formula: see text]-fault-tolerant one-to-many maximally local-connected if [Formula: see text] does not contain [Formula: see text] and is super [Formula: see text]-vertex-connected of order 1.

Performance Evaluation, Comparison and Identification of Efficient Hypercube Interconnection Networks

2021 ◽  
Author(s):  
Karthik K ◽  
Sudarson Jena ◽  
Venu Gopal T
Keyword(s):  
Interconnection Networks ◽  
Interconnection Network ◽  
Research Work ◽  
Processing Unit ◽  
Network Cost ◽  
Multi Stage ◽  
Memory Modules ◽  
Effective Performance ◽  
Twisted Cube ◽  
Hypercube Network

Abstract 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.

THE CUBE-OF-RINGS INTERCONNECTION NETWORK

1998 ◽  
Vol 09 (01) ◽  
pp. 25-37 ◽  
Author(s):  
THOMAS J. CORTINA ◽  
ZHIWEI XU
Keyword(s):  
Graph Theory ◽  
Interconnection Networks ◽  
Fault Tolerant ◽  
Interconnection Network ◽  
Routing Algorithm ◽  
Parallel Computers ◽  
Closed Form Expression ◽  
Form Expression ◽  
Graph Theoretic ◽  
Basic Graph

We present a family of interconnection networks named the Cube-Of-Rings (COR) networks along with their basic graph-theoretic properties. Aspects of group graph theory are used to show the COR networks are symmetric and optimally fault tolerant. We present a closed-form expression of the diameter and optimal one-to-one routing algorithm for any member of the COR family. We also discuss the suitability of the COR networks as the interconnection network of scalable parallel computers.

Designing a New Class of Fault Tolerant Multistage Interconnection Networks

2005 ◽  
Vol 06 (04) ◽  
pp. 361-382 ◽  
Author(s):  
K. V. Arya ◽  
R. K. Ghosh
Keyword(s):  
Fault Tolerance ◽  
Interconnection Networks ◽  
Fault Tolerant ◽  
Interconnection Network ◽  
Multistage Interconnection Networks ◽  
Multistage Interconnection Network ◽  
New Class

This paper proposes a technique to modify a Multistage Interconnection Network (MIN) to augment it with fault tolerant capabilities. The augmented MIN is referred to as Enhanced MIN (E-MIN). The technique employed for construction of E-MIN is compared with the two known physical fault tolerance techniques, namely, extra staging and chaining. EMINs are found to be more generic than extra staged networks and less expensive than chained networks. The EMIN realizes all the permutations realizable by the original MIN. The routing strategies under faulty and fault free conditions are shown to be very simple in the case of E-MINs.

scholarly journals Topological Properties of Hierarchical Interconnection Networks: A Review and Comparison

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Mostafa Abd-El-Barr ◽  
Turki F. Al-Somani
Keyword(s):  
Packing Density ◽  
Interconnection Networks ◽  
Fault Tolerant ◽  
Interconnection Network ◽  
Parallel Applications ◽  
Topological Properties ◽  
Remote Communication ◽  
Chip Area ◽  
Network Diameter ◽  
Link Cost

Hierarchical interconnection networks (HINs) provide a framework for designing networks with reduced link cost by taking advantage of the locality of communication that exists in parallel applications. HINs employ multiple levels. Lower-level networks provide local communication while higher-level networks facilitate remote communication. HINs provide fault tolerance in the presence of some faulty nodes and/or links. Existing HINs can be broadly classified into two classes. those that use nodes and/or links replication and those that use standby interface nodes. The first class includes Hierarchical Cubic Networks, Hierarchical Completely Connected Networks, and Triple-based Hierarchical Interconnection Networks. The second HINs class includes Modular Fault-Tolerant Hypercube Networks and Hierarchical Fault-Tolerant Interconnection Network. This paper presents a review and comparison of the topological properties of both classes of HINs. The topological properties considered are network degree, diameter, cost and packing density. The outcome of this study show among all HINs two networks that is, the Root-Folded Heawood (RFH) and the Flooded Heawood (FloH), belonging to the first HIN class provide the best network cost, defined as the product of network diameter and degree. The study also shows that HFCube(n,n)provide the best packing density, that is, the smallest chip area required for VLSI implementation.

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