Fault-tolerant of Bubble-sort Star Graph Based on Subgraph Fault Pattern

An interconnection network is usually modeled by a connected graph in which vertices represent processors and edges represent links between processors. The connectivity is an important parameter to evaluate the fault tolerance of interconnection networks. A connected graph [Formula: see text] is maximally local-(edge-)connected if each pair vertices [Formula: see text] of [Formula: see text] is connected by min[Formula: see text] pairwise (edge-)disjoint paths between [Formula: see text] and [Formula: see text] in [Formula: see text]. A graph [Formula: see text] is called [Formula: see text]-fault-tolerant maximally local-(edge-)connected if [Formula: see text] is maximally local-(edge-)connected for any [Formula: see text] ([Formula: see text]) with [Formula: see text]. A graph [Formula: see text] is called [Formula: see text]-fault-tolerant maximally local-(edge-)connected of order [Formula: see text] if [Formula: see text] is maximally local-(edge-)connected for any [Formula: see text] with [Formula: see text], where [Formula: see text] is a conditional faulty vertex (edge) set of order [Formula: see text]. In this paper, we obtain the sufficient condition of connected graphs to be [Formula: see text]-edge-fault-tolerant maximally local-edge-connected. Moreover, we consider the sufficient condition of connected graphs to be [Formula: see text]-fault-tolerant maximally local-(edge-)connected of order [Formula: see text]. Some previous results in [Theor. Comput. Sci. 731 (2018) 50–67] and [Theor. Comput. Sci. 847 (2020) 39–48] are extended.

Edge fault tolerance of interconnection networks with respect to maximally edge-connectivity

Today, high-performance computing is recognized as a necessity in various industries. The stable and secure connection between system components, such as CPUs and memories, requires efficient, reliable, and fault-tolerant networks. Multistage Interconnection Networks (MIN) are fundamental approaches to create such an interconnection facility among researchers and engineers. Meanwhile, the Gamma Interconnection Network (GIN) provides one of the highest levels of fault tolerance networks among MINs by establishing multiple paths. Considering the importance of disjoint paths, 4-Disjoint GIN (4DGIN) has been developed, which is an important type of GIN and provides four disjoint paths for all source–destination pairs. On the other hand, the replication approach improves network fault tolerance, which directly affects network reliability. In this paper, a replicated 4DGIN is proposed, enhancing the reliability and improving the fault-tolerance factor by creating disjoint and redundant paths. The reliability of the proposed network is evaluated using the Reliability Block Diagram (RBD) approach. The reliability evaluation results show that the proposed network outperforms several well-known MINs, such as different variations of SEN and Benes networks in terms of the terminal, broadcast, and network reliability factors. Moreover, it improves the cost per unit factor in comparison with the baselines.

Processor and communication link failures are inevitable in a large multiprocessor system, and so the fault tolerance of its underlying interconnection network has become a key scientific issue. Connectivity is an important parameter to characterize network fault tolerance, and there are many novel variants of classical connectivity to measure the fault tolerance of interconnection networks. However, these new strategies only consider a single faulty vertex. Structure connectivity and substructure connectivity make up for this deficiency, which underline the fault situation with certain specific structures. H-structure-connectivity κ ( G ; H ) (resp. H-substructure-connectivity κ s ( G ; H ) ) of G is the minimum cardinality of H-structure-cuts (resp. H-substructure-cuts). For the n-dimensional Bicube network B Q n , we establish the structure and substructure connectivity of Bicube networks, i.e. κ ( B Q n ; K 1 , 1 ) = κ s ( B Q n ; K 1 , 1 ) = n for odd n ≥ 5 ; κ ( B Q n ; K 1 , 1 ) = κ s ( B Q n ; K 1 , 1 ) = n − 1 for even n ≥ 4 and κ ( B Q n ; K 1 , r ) = κ s ( B Q n ; K 1 , r ) = ⌈ n 2 ⌉ for n ≥ 6 and 2 ≤ r ≤ n − 1 .

Fault tolerance analysis of the class of rearrangeable interconnection networks

Many-to-many edge-disjoint paths in (n,k)-enhanced hypercube under three link-faulty hypotheses

Connectivity is an important measurement for the fault tolerance in interconnection networks. It is known that the augmented cube AQ n is maximally connected, i.e. (2n - 1)-connected, for n ≥ 4. By the classical Menger’s Theorem, every pair of vertices in AQ n is connected by 2n - 1 vertex-disjoint paths for n ≥ 4. A routing with parallel paths can speed up transfers of large amounts of data and increase fault tolerance. Motivated by some research works on networks with faults, we have a further result that for any faulty vertex set F ⊂ V(AQ n ) and |F| ≤ 2n − 7 for n ≥ 4, each pair of non-faulty vertices, denoted by u and v, in AQ n − F is connected by min{deg f (u), deg f (v)} vertex-disjoint fault-free paths, where deg f (u) and deg f (v) are the degree of u and v in AQ n − F, respectively. Moreover, we have another result that for any faulty vertex set F ⊂ V(AQ n ) and |F| ≤ 4n − 9 for n ≥ 4, there exists a large connected component with at least 2n − |F| − 1 vertices in AQ n − F. In general, a remaining large fault-free connected component also increases fault tolerance.Keywordsconnectivitylocal connectivityfault tolerancevertex-disjoint pathaugmented cube

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.

In fault-tolerant interconnection designs, many prior researches suggest good use of disjoint paths to improve the reliability of interconnection networks. Although disjoint paths increase reliability, they always cost the throughput penalty. To address the problems of both performance and fault-tolerant capability, the following issues should be carefully considered: (1) guarantee of at least two disjoint paths, (2) easy rerouting between disjoint paths, (3) keep low rerouting hops, (4) solve the occurrences of packets' collision. In this paper, we consider these issues to design a fault-tolerant network called CSMIN (Combining Switches Multistage Interconnection Network). CSMIN provides two disjoint paths to guarantee one fault-tolerant and can dynamically reroute packets between these two paths to solve the collision situation. In other words, to switch packets between these two disjoint paths easily, CSMIN causes these two disjoint paths to have regular distances at each stage. Accordingly, a packet can be dynamically sent to the other disjoint path if it encounters a faulty or busy element. In addition, CSMIN presents low rerouting hops (an average of one rerouting hop) to maintain a low collision ratio. From the simulation result, CSMIN performs with a better arrival ratio than Gamma and other related disjoint paths networks do.

Connectivity and diagnosability of the complete Josephus cube networks under h-extra fault-tolerant model

The 2-good-neighbor connectivity and 2-good-neighbor diagnosability of bubble-sort star graph networks

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.

High-performance supercomputers generally comprise millions of CPUs in which interconnection networks play an important role to achieve high performance. New design paradigms of dynamic on-chip interconnection network involve a) topology b) synthesis, modeling and evaluation c) quality of service, fault tolerance and reliability d) routing procedures. To construct a dynamic highly fault tolerant interconnection networks requires more disjoint paths from each source-destination node pair at each stage and dynamic rerouting capability to use the various available paths effectively. Fast routing and rerouting strategy is needed to provide reliable performance on switch/link failures. This paper proposes two new architecture designs of fault tolerant interconnection networks named as reliable interconnection networks (RIN-1 and RIN-2). The proposed layouts are multipath multi-stage interconnection networks providing four disjoint paths for all the source-destination node pairs with dynamic rerouting capability. The designs can withstand switch failures in all the stages (including input and output stages) and provide more reliability. Reliability analysis of various MIN architectures is evaluated. On comparing the results with some existing MINs it is evident that the proposed designs provides higher reliability values and fault tolerance.

Conditional connectivity has been proposed as an important parameter to estimate the fault tolerance of interconnection networks. In this paper, we consider the conditional connectivity of (n, k)-star graph. An (n, k)-star graph with dimension n (n ≥ 4) and order k can be partitioned into n subgraphs,. By utilizing this property, we give and proof the minimal cut-set and the minimal conditional cut-set of S n,k. We hence obtain that the conditional connectivity of (n, k)-star graph S n,k is n+k−3.

Diagnosability is an important parameter to measure the fault tolerance of interconnection networks. Arrangement graph is a generalisation of the star graphs, yet it is more flexible in its size than the star graphs. In this paper, we study the local diagnosability of , and show that it has the strong local diagnosability property even if there exist missing edges in it under the MM* model, and the result is optimal with respect to the number of missing edges.