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.

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.

FAULT-TOLERANT MAXIMAL LOCAL-CONNECTIVITY ON CAYLEY GRAPHS GENERATED BY TRANSPOSITION TREES

2009 ◽  
Vol 10 (03) ◽  
pp. 253-260 ◽  
Author(s):  
LUN-MIN SHIH ◽  
CHIEH-FENG CHIANG ◽  
LIH-HSING HSU ◽  
JIMMY J. M. TAN
Keyword(s):  
Cayley Graph ◽  
Fault Tolerant ◽  
Minimum Degree ◽  
Cayley Graphs ◽  
Disjoint Paths ◽  
Local Connectivity ◽  
Vertex Disjoint

The local connectivity of two vertices is defined as the maximum number of internally vertex-disjoint paths between them. In this paper, we define two vertices as maximally local-connected, if the maximum number of internally vertex-disjoint paths between them equals the minimum degree of these two vertices. Moreover, we show that an (n-1)-regular Cayley graph generated by transposition tree is maximally local-connected, even if there are at most (n-3) faulty vertices in it, and prove that it is also (n-1)-fault-tolerant one-to-many maximally local-connected.

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.  

Internally Vertex-Disjoint Paths in Crossed Cube-Connected Ring Networks

2013 ◽  
Vol 321-324 ◽  
pp. 2715-2720
Author(s):  
Xin Yu ◽  
Gao Cai Wang ◽  
Yan Yu
Keyword(s):  
Interconnection Networks ◽  
Interconnection Network ◽  
Disjoint Paths ◽  
Ring Networks ◽  
Vertex Disjoint ◽  
Crossed Cube

Crossed cube is a variation of hypercube, but some properties of the former are superior to those of the latter. However, it is difficult to extend the scale of crossed cube networks. As a kind of hierarchical ring interconnection networks, crossed cube-connected ring interconnection network CRN can effectively overcome the disadvantage. Hence, it is a good topology for interconnection networks. In this paper, we prove that there exist n internally vertex-disjoint paths between any two vertexes in CRN, and analyze the lengths of the paths.

A novel design layout of three disjoint paths multistage interconnection network & its reliability analysis

2021 ◽  
Vol 17 (4) ◽  
pp. 390-403
Author(s):  
Vipin Sharma ◽  
Abdul Q. Ansari ◽  
Rajesh Mishra
Keyword(s):  
Fault Tolerance ◽  
Interconnection Networks ◽  
Interconnection Network ◽  
High Reliability ◽  
Block Diagram ◽  
Low Cost ◽  
Disjoint Paths ◽  
Content Type ◽  
Multistage Interconnection Network ◽  
Terminal Reliability

Purpose The purpose of this paper is to design a efficient layout of Multistage interconnection network which has cost effective solution with high reliability and fault-tolerence capability. For parallel computation, various multistage interconnection networks (MINs) have been discussed hitherto in the literature, however, these networks always required further improvement in reliability and fault-tolerance capability. The fault-tolerance capability of the network can be achieved by increasing the number of disjoint paths as a result the reliability of the interconnection networks is also improved. Design/methodology/approach This proposed design is a modification of gamma interconnection network (GIN) and three disjoint path gamma interconnection network (3-DGIN). It has a total seven number of paths for all tag values which is uniform out of these seven paths, three paths are disjoint paths which increase the fault tolerance capability by two faults. Due to the presence of more paths than the GIN and 3-DGIN, this proposed design is more reliable. Findings In this study, a new design layout of a MIN has been proposed which provides three disjoint paths and uniformity in terms of an equal number of paths for all source-destination (S-D) pairs. The new layout contains fewer nodes as compared to GIN and 3-DGIN. This design provides a symmetrical structure, low cost, better terminal reliability and provides an equal number of paths for all tag values (|S-D|) when compared with existing MINs of this class. Originality/value A new design layout of MINs has been purposed and its two terminal reliability is calculated with the help of the reliability block diagram technique.

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.

scholarly journals The Edge Connectivity of Expanded k-Ary n-Cubes

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Shiying Wang ◽  
Mujiangshan Wang
Keyword(s):  
Fault Tolerance ◽  
Interconnection Networks ◽  
Interconnection Network ◽  
Complex Problem ◽  
Multiprocessor System ◽  
Multiprocessor Systems ◽  
Complex Problem Solving ◽  
Edge Connectivity ◽  
Communication Links ◽  
Minimum Number

Mass data processing and complex problem solving have higher and higher demands for performance of multiprocessor systems. Many multiprocessor systems have interconnection networks as underlying topologies. The interconnection network determines the performance of a multiprocessor system. The network is usually represented by a graph where nodes (vertices) represent processors and links (edges) represent communication links between processors. For the network G, two vertices u and v of G are said to be connected if there is a (u,v)-path in G. If G has exactly one component, then G is connected; otherwise G is disconnected. In the system where the processors and their communication links to each other are likely to fail, it is important to consider the fault tolerance of the network. For a connected network G=(V,E), its inverse problem is that G-F is disconnected, where F⊆V or F⊆E. The connectivity or edge connectivity is the minimum number of F. Connectivity plays an important role in measuring the fault tolerance of the network. As a topology structure of interconnection networks, the expanded k-ary n-cube XQnk has many good properties. In this paper, we prove that (1) XQnk is super edge-connected (n≥3); (2) the restricted edge connectivity of XQnk is 8n-2 (n≥3); (3) XQnk is super restricted edge-connected (n≥3).

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.

Subgraph-based Strong Menger Connectivity of Hypercube and Exchanged Hypercube

2021 ◽  
pp. 1-26
Author(s):  
Yihong Wang ◽  
Cheng-Kuan Lin ◽  
Shuming Zhou ◽  
Tao Tian
Keyword(s):  
Big Data ◽  
Fault Tolerance ◽  
Connected Graph ◽  
Interconnection Networks ◽  
Large Scale ◽  
Fault Tolerant ◽  
Disjoint Paths ◽  
Multiprocessor Systems ◽  
Edge Disjoint ◽  
Cube Formula

Large scale multiprocessor systems or multicomputer systems, taking interconnection networks as underlying topologies, have been widely used in the big data era. Fault tolerance is becoming an essential attribute in multiprocessor systems as the number of processors is getting larger. A connected graph [Formula: see text] is called strong Menger (edge) connected if, for any two distinct vertices [Formula: see text] and [Formula: see text], there are [Formula: see text] vertex (edge)-disjoint paths between them. Exchanged hypercube [Formula: see text], as a variant of hypercube [Formula: see text], remains lots of preferable fault tolerant properties of hypercube. In this paper, we show that [Formula: see text] [Formula: see text] and [Formula: see text] [Formula: see text] are strong Menger (edge) connected, respectively. Moreover, as a by-product, for dual cube [Formula: see text], one popular generalization of hypercube, [Formula: see text] is also showed to be strong Menger (edge) connected, where [Formula: see text].

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