scholarly journals Cluster-Fault Tolerant Routing in a Torus

Sensors ◽  
2020 ◽  
Vol 20 (11) ◽  
pp. 3286 ◽  
Author(s):  
Antoine Bossard ◽  
Keiichi Kaneko
Keyword(s):  
Free Path ◽  
Time Complexity ◽  
Fault Tolerant ◽  
Interconnection Network ◽  
Routing Algorithm ◽  
Topological Properties ◽  
Huge Number ◽  
Worst Case ◽  
Faulty Node ◽  
Node Routing

The number of Internet-connected devices grows very rapidly, with even fears of running out of available IP addresses. It is clear that the number of sensors follows this trend, thus inducing large sensor networks. It is insightful to make the comparison with the huge number of processors of modern supercomputers. In such large networks, the problem of node faults necessarily arises, with faults often happening in clusters. The tolerance to faults, and especially cluster faults, is thus critical. Furthermore, thanks to its advantageous topological properties, the torus interconnection network has been adopted by the major supercomputer manufacturers of the recent years, thus proving its applicability. Acknowledging and embracing these two technological and industrial aspects, we propose in this paper a node-to-node routing algorithm in an n -dimensional k -ary torus that is tolerant to faults. Not only is this algorithm tolerant to faulty nodes, it also tolerates faulty node clusters. The described algorithm selects a fault-free path of length at most n ( 2 k + ⌊ k / 2 ⌋ − 2 ) with an O ( n 2 k 2 | F | ) worst-case time complexity with F the set of faulty nodes induced by the faulty clusters.

OPTIMUM CONGESTED ROUTING STRATEGY ON TWISTED CUBES

2000 ◽  
Vol 01 (02) ◽  
pp. 115-134 ◽  
Author(s):  
TSENG-KUEI LI ◽  
JIMMY J. M. TAN ◽  
LIH-HSING HSU ◽  
TING-YI SUNG
Keyword(s):  
Shortest Path ◽  
Time Complexity ◽  
Interconnection Network ◽  
Routing Algorithm ◽  
Optimum Time ◽  
Shortest Path Routing ◽  
Routing Strategy ◽  
Bisection Width ◽  
Twisted Cube ◽  
Twisted Cubes

Given a shortest path routing algorithm of an interconnection network, the edge congestion is one of the important factors to evaluate the performance of this algorithm. In this paper, we consider the twisted cube, a variation of the hypercube with some better properties, and review the existing shortest path routing algorithm8. We find that its edge congestion under the routing algorithm is high. Then, we propose a new shortest path routing algorithm and show that our algorithm has optimum time complexity O(n) and optimum edge congestion 2n. Moreover, we calculate the bisection width of the twisted cube of dimension n.

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.

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.

Analysis the Performance of Interconnection Network Topology C2 Torus Based on Two Dimensional Torus

2018 ◽  
Vol 6 (6) ◽  
pp. 169 ◽  
Author(s):  
Prachi Chauhan ◽  
Manish Bhardwaj
Keyword(s):  
Network Topology ◽  
Interconnection Network ◽  
Routing Algorithm ◽  
Two Dimensional ◽  
Topological Properties ◽  
Interconnected Network ◽  
Dimensional Torus ◽  
Torus Network

Mesh and Torus are most popular interconnection topologies based on 2D-mesh.Comparison between Mesh and Torus will be considered and new interconnection topology will be proposed to provide better performance. The C2Mesh, is an enhanced mesh interconnected network. This paper enhances the torus network based on the theme of C2Mesh. Topological Properties of new network will be analyzed and implemented by simulation. The new routing Algorithm will be designed for new proposed network (C2Torus). This manuscript performs Comparison between C2Torus and C2Mesh.

NEARLY OPTIMAL NODE-TO-SET PARALLEL ROUTING IN OTIS NETWORKS

2012 ◽  
Vol 13 (01n02) ◽  
pp. 1250002
Author(s):  
WEIDONG CHEN ◽  
WENJUN XIAO ◽  
BEHROOZ PARHAMI
Keyword(s):  
Time Complexity ◽  
Fault Tolerant ◽  
Routing Algorithm ◽  
Practical Interest ◽  
Hierarchical Structures ◽  
Optimal Time ◽  
Routing Problem ◽  
Shortest Path Routing ◽  
Node Factor ◽  
General Network

The node-to-set parallel routing problem for a k-connected network Γ is as follows: given a node s and k other nodes {t1, t2, … , tk} in Γ, find k node-disjoint paths connecting s and ti, for 1 ≤ i ≤ k. From the viewpoint of applications in synthesizing fast and resilient collective communication operations, it is desirable to make the parallel paths as short as possible. Building such paths is a nontrivial problem for a general network. Optical transpose interconnection system (OTIS, also known as swapped) networks, a class of hierarchical structures built of n identical n-node factor networks, are known to be maximally fault-tolerant for any connected factor network, implying that they have maximal connectivity. We propose a general algorithm for the node-to-set parallel routing problem in OTIS/swapped networks that yields paths of length no greater than D + 4 in O(Δ2 + Δf(n)) time, where D and Δ represent the diameter and degree of the OTIS network and O(f(n)) is the time complexity of a shortest-path routing algorithm for the n-node factor network. Our node-to-set routing algorithm is shown to have optimal time complexity for certain OTIS networks of practical interest, including OTIS-Mesh and OTIS-Hypercube.

scholarly journals Message Broadcasting via a New Fault Tolerant Irregular Advance Omega Network in Faulty and Nonfaulty Network Environments

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Ved Prakash Bhardwaj ◽  
Nitin
Keyword(s):  
Fault Tolerant ◽  
Interconnection Network ◽  
High Reliability ◽  
Low Cost ◽  
Routing Algorithm ◽  
Multiple Faults ◽  
Message Broadcasting ◽  
Double Switch ◽  
Better Than

Interconnection Network (IN) is a key element for all parallel processing applications. Multistage Interconnection Network (MIN) is an efficient IN for these applications, as it has the quality of excellent performance at low cost with high reliability. MINs are effective medium for message broadcasting. Doing the same task in faulty situations is a critical challenge. In this paper, we have presented a new Fault Tolerant Interconnection Network named as Irregular Advance Omega Network (IAON); also we have presented its routing algorithm. IAON is the modified form of Advance Omega Network. The proposed MIN can endure multiple faults and provides a suitable path between every source to every destination. We have examined the fault tolerance capacity of IAON and compared its performance with other existing MINs. In order to check the performance of proposed MIN, message broadcasting was performed in three conditions as follows: (1) when network was fault free; (2) when network was Single Switch Faulty in every stage; (3) when network was Double Switch Faulty in every stage. Results showed that IAON performed better than the earlier proposed MINs.

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.

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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