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.

scholarly journals Reliable, Effective and Fault-Tolerant Design of Leafy Cube Interconnection Network Topology

2019 ◽  
Vol 8 (12) ◽  
pp. 3163-3170
Keyword(s):  
Cost Effectiveness ◽  
Network Topology ◽  
Packing Density ◽  
Fault Tolerant ◽  
Interconnection Network ◽  
The Other ◽  
Performance Parameters ◽  
Topological Properties ◽  
Node Packing ◽  
The Cost

This paper attempts to derive the performance properties of the Leafycube (LC) interconnection network. The Leafycube is already observed to have quite superior topological properties in comparison to the other contemporary networks. The various performance parameters of the LC network are studied and compared with the existing HC and its variants. The routing and broadcasting algorithms are proposed and the time complexities are also compared. The paper attempts to evaluate the cost effectiveness, reliability and fault tolerance aspects of LC interconnection network in order to justify the novelty in the design of the proposed structure. The leafy structure helps to retain the original hypercube while improving the node packing density in the interconnection network.

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 Conditional Fault-Diameter of Torus Networks

2005 ◽  
Vol 10 ◽  
pp. 51
Author(s):  
Abderezak Touzene ◽  
Khaled Day
Keyword(s):  
Interconnection Networks ◽  
Fault Tolerant ◽  
Interconnection Network ◽  
Routing Algorithms ◽  
Star Graph ◽  
Faulty Processor ◽  
Node Connectivity ◽  
Fault Diameter ◽  
Torus Networks ◽  
Vertex Disjoint

We obtain the conditional fault-diameter of the square torus interconnection network under the condition of forbidden faulty sets (i.e. assuming that each non-faulty processor has at least one non-faulty neighbor). We show that under this condition, the square torus, whose connectivity is 4, can tolerate up to 5 faulty nodes without becoming disconnected. The conditional node connectivity is, therefore, 6. We also show that the conditional fault-diameter of the square torus is equal to the fault-free diameter plus two. With this result the torus joins a group of interconnection networks (including the hypercube and the star-graph) whose conditional fault-diameter has been shown to be only two units over the fault-free diameter. Two fault-tolerant routing algorithms are discussed based on the proposed vertex disjoint paths construction.  

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.

EMBEDDING OF FAULT-TOLERANT TREES IN THE JOSEPHUS CUBE

2002 ◽  
Vol 12 (01) ◽  
pp. 3-16
Author(s):  
PETER K. K. LOH ◽  
W. J. HSU
Keyword(s):  
Traffic Congestion ◽  
Interconnection Networks ◽  
Fault Tolerant ◽  
Interconnection Network ◽  
Single Point ◽  
Research Interest ◽  
Tree Network ◽  
Root Node ◽  
Reliability And Availability

The tree interconnection network lends itself to several suitably structured applications. However, the low connectivity at each node, traffic congestion and single point of failure at the root node reduce reliability and availability. Both the hypertree and X-tree are fault-tolerant variants of the basic tree network and have been the focus of more recent implementation and research interest. In this paper, we consider a recently proposed family of interconnection networks known as the Josephus Cubes and show how hypertrees, X-trees and ringed X-trees of arbitrary height can be near-optimally embedded in this novel interconnection network.

scholarly journals A Novel Tradeoff Analysis between Traffic Congestion and Packing Density of Interconnection Networks for Massively Parallel Computers

2021 ◽  
Vol 11 (22) ◽  
pp. 10798
Author(s):  
M. M. Hafizur Rahman ◽  
Mohammed Al-Naeem ◽  
Mohammed Mustafa Ghowanem ◽  
Eklas Hossain
Keyword(s):  
Packing Density ◽  
Traffic Congestion ◽  
Interconnection Networks ◽  
Network Performance ◽  
Interconnection Network ◽  
Future Generation ◽  
Parallel Computer ◽  
Massively Parallel ◽  
Traffic Density ◽  
Trade Off

From disaster prevention to mitigation, drug analysis to drug design, agriculture to food security, IoT to AI, and big data analysis to knowledge or sentiment mining, a high computation power is a prime necessity at present. As such, massively parallel computer (MPC) systems comprising a large number of nodes are gaining popularity. To interconnect these huge numbers of nodes efficiently, hierarchical interconnection networks are an attractive and feasible option. A Tori-connected flattened butterfly network (TFBN) has been proposed by the authors in a prior work for future generation MPC systems. In the previous study, the static network performance and static cost-effectiveness were evaluated. In this research, a novel trade-off factor named message traffic congestion vs. packing density trade-off factor has been proposed, which characterizes the message congestion in the network and its packing density. The factor is used to statically assess the suitability of the implementation of an interconnection network. The message traffic density, packing density, and new factor have been evaluated for the proposed network and similar competitive networks such as TTN, TESH, 2D-Mesh, 3D-Mesh, 2D-Torus, and 3D-Torus. It has been found that the performance of the TFBN is superior to the other networks.

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.

Fault-Tolerant Routing in Wormhole Meshes

2003 ◽  
Vol 04 (04) ◽  
pp. 463-495 ◽  
Author(s):  
Ming-Jer Tsai
Keyword(s):  
Interconnection Networks ◽  
Fault Tolerant ◽  
Interconnection Network ◽  
Routing Algorithm ◽  
Fixed Number ◽  
One Dimension ◽  
Global Information ◽  
Unlimited Number ◽  
Fully Adaptive

In wormhole meshes, many a routing algorithm prevents a deadlock by enclosing unlimited number of faulty nodes with faulty blocks and dividing a physical interconnection network into a fixed number of virtual ones; none of them, however, is able to tolerate two faulty blocks with a distance of two, no less, in at least one dimension by use of only two virtual interconnection networks. To fill this gap, an adaptive and fault-tolerant routing algorithm is proposed. The algorithm is fully-adaptive until encountering a faulty block. It then detours the blocked message around the faulty block. Arranging the detours around faulty blocks attempts to prevent a deadlock. The proposed method has no need for global information.

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