Minimum number of links needed for fault-tolerance in cluster-based network

1991 ◽  
Author(s):  
K. Ishida ◽  
T. Kikuno
Keyword(s):  
Fault Tolerance ◽  
Minimum Number

Component Edge Connectivity of Hypercubes

2018 ◽  
Vol 29 (06) ◽  
pp. 995-1001 ◽  
Author(s):  
Shuli Zhao ◽  
Weihua Yang ◽  
Shurong Zhang ◽  
Liqiong Xu
Keyword(s):  
Fault Tolerance ◽  
Complete Graph ◽  
Interconnection Networks ◽  
Interconnection Network ◽  
Optimal Solutions ◽  
Edge Connectivity ◽  
Important Measure ◽  
Minimum Number ◽  
Text Component

Fault tolerance is an important issue in interconnection networks, and the traditional edge connectivity is an important measure to evaluate the robustness of an interconnection network. The component edge connectivity is a generalization of the traditional edge connectivity. The [Formula: see text]-component edge connectivity [Formula: see text] of a non-complete graph [Formula: see text] is the minimum number of edges whose deletion results in a graph with at least [Formula: see text] components. Let [Formula: see text] be an integer and [Formula: see text] be the decomposition of [Formula: see text] such that [Formula: see text] and [Formula: see text] for [Formula: see text]. In this note, we determine the [Formula: see text]-component edge connectivity of the hypercube [Formula: see text], [Formula: see text] for [Formula: see text]. Moreover, we classify the corresponding optimal solutions.

scholarly journals Minimum survivable graphs with bounded distance increase

2003 ◽  
Vol Vol. 6 no. 1 ◽  
Author(s):  
Selma Djelloul ◽  
Mekkia Kouider
Keyword(s):  
Fault Tolerance ◽  
Lower Bounds ◽  
Interconnection Networks ◽  
Negative Integer ◽  
Upper And Lower Bounds ◽  
Minimum Size ◽  
Np Hard ◽  
Bounded Distance ◽  
Minimum Number ◽  
International Audience

International audience We study in graphs properties related to fault-tolerance in case a node fails. A graph G is k-self-repairing, where k is a non-negative integer, if after the removal of any vertex no distance in the surviving graph increases by more than k. In the design of interconnection networks such graphs guarantee good fault-tolerance properties. We give upper and lower bounds on the minimum number of edges of a k-self-repairing graph for prescribed k and n, where n is the order of the graph. We prove that the problem of finding, in a k-self-repairing graph, a spanning k-self-repairing subgraph of minimum size is NP-Hard.

On Component Connectivity of Hierarchical Star Networks

2020 ◽  
Vol 31 (03) ◽  
pp. 313-326
Author(s):  
Mei-Mei Gu ◽  
Jou-Ming Chang ◽  
Rong-Xia Hao
Keyword(s):  
Fault Tolerance ◽  
Network Topology ◽  
Interconnection Network ◽  
Building Blocks ◽  
Star Graphs ◽  
Combinatorial Properties ◽  
Star Networks ◽  
Minimum Number ◽  
Text Component ◽  
Disconnected Graph

For an integer [Formula: see text], the [Formula: see text]-component connectivity of a graph [Formula: see text], denoted by [Formula: see text], is the minimum number of vertices whose removal from [Formula: see text] results in a disconnected graph with at least [Formula: see text] components or a graph with fewer than [Formula: see text] vertices. This naturally generalizes the classical connectivity of graphs defined in term of the minimum vertex-cut. This kind of connectivity can help us to measure the robustness of the graph corresponding to a network. The hierarchical star networks [Formula: see text], proposed by Shi and Srimani, is a new level interconnection network topology, and uses the star graphs as building blocks. In this paper, by exploring the combinatorial properties and fault-tolerance of [Formula: see text], we study the [Formula: see text]-component connectivity of hierarchical star networks [Formula: see text]. We obtain the results: [Formula: see text], [Formula: see text] and [Formula: see text] for [Formula: see text].

scholarly journals Fast Reliability Assessment of Neutral-Point-Clamped Topologies through Markov Models

2020 ◽  
Author(s):  
Sergio Busquets-Monge ◽  
Roya Rafiezadeh ◽  
Salvador Alepuz ◽  
Alber Filba-Martinez ◽  
Joan Nicolas-Apruzzese
Keyword(s):  
Fault Tolerance ◽  
Markov Models ◽  
Reliability Assessment ◽  
Open Circuit ◽  
Neutral Point ◽  
Time To Failure ◽  
Fast Calculation ◽  
Reliability Models ◽  
Minimum Number ◽  
Mean Time

This paper presents detailed Markov models for the reliability assessment of multilevel neutral-point-clamped (NPC) converter leg topologies, incorporating their inherent fault-tolerance under open-circuit switch faults. The Markov models are generated and discussed in detail for the three-level and four-level active NPC (ANPC) cases, while the presented methodology can be applied to easily generate the models for higher number of levels and for other topology variants. In addition, this paper also proposes an extremely fast calculation method to obtain the precise value of the system mean time to failure from any given formulated system Markov model. This method is then applied to quantitatively compare the reliability of two-level, three-level, and four-level ANPC legs under switch open-circuit-guaranteed faults and varying degrees of device paralleling. The comparison reveals that multilevel ANPC leg topologies inherently present a potential for a higher reliability than the conventional two-level leg, questioning the suitability of the traditional search for topologies with the minimum number of devices in order to improve reliability. Experimental results are presented to validate the fault-tolerance assumptions upon which the presented reliability models for the three-level and four-level ANPC legs are based.

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).

The g-Extra Conditional Diagnosability of Graphs in Terms of g-Extra Connectivity

2020 ◽  
Vol 30 (03) ◽  
pp. 2040006
Author(s):  
Aixia Liu ◽  
Jun Yuan ◽  
Shiying Wang
Keyword(s):  
Fault Tolerance ◽  
Multiprocessor System ◽  
Minimum Number ◽  
Number Formula ◽  
Conditional Diagnosability

The [Formula: see text]-extra conditional diagnosability and [Formula: see text]-extra connectivity are two important parameters to measure ability of diagnosing faulty processors and fault tolerance in a multiprocessor system. The [Formula: see text]-extra conditional diagnosability [Formula: see text] of graph [Formula: see text] is defined as the diagnosability of a multiprocessor system under the assumption that every fault-free component contains more than [Formula: see text] vertices. While the [Formula: see text]-extra connectivity [Formula: see text] of graph [Formula: see text] is the minimum number [Formula: see text] for which there is a vertex cut [Formula: see text] with [Formula: see text] such that every component of [Formula: see text] has more than [Formula: see text] vertices. In this paper, we study the [Formula: see text]-extra conditional diagnosability of graph [Formula: see text] in terms of its [Formula: see text]-extra connectivity, and show that [Formula: see text] under the MM* model with some acceptable conditions. As applications, the [Formula: see text]-extra conditional diagnosability is determined for some BC networks such as hypercubes, varietal hypercubes, and [Formula: see text]-ary [Formula: see text]-cubes under the MM* model.

ON FAULT TOLERANCE OF HYPERCUBES USING SUBCUBES

2002 ◽  
Vol 09 (02) ◽  
pp. 151-161 ◽  
Author(s):  
TOSHIHIKO SASAMA ◽  
HIROSHI MASUYAMA ◽  
TETSUO ICHIMORI
Keyword(s):  
Fault Tolerance ◽  
Upper Bound ◽  
Distributed Processing ◽  
Parallel And Distributed Processing ◽  
Minimum Number

A hypercube is an important interconnection topology in parallel and distributed processing. This paper treats fault tolerance of a hypercube. More precisely, it discusses relations between a faulty hypercube and its fault-free subcubes. First, this paper presents an upper bound on the minimum number of faults in an n-cube where no fault-free (n - m)-subcube can exist. Next, it is shown that the bound can be improved if m = 2. Finally, the paper discusses the number of faults when there are always at least two fault-free disjoint (n - 2)-subcubes.

Reliability Evaluation of Augmented Cubes on Degree

2021 ◽  
Author(s):  
Mingzu Zhang ◽  
Xiaoli Yang ◽  
Xiaomin He ◽  
Zhuangyan Qin ◽  
Yongling Ma
Keyword(s):  
Fault Tolerance ◽  
Interconnection Networks ◽  
Minimum Degree ◽  
Tolerance Analysis ◽  
Reliability Evaluation ◽  
Affirmative Answer ◽  
Edge Connectivity ◽  
Minimum Number ◽  
Edge Fault Tolerance ◽  
Augmented Cube

The [Formula: see text]-dimensional augmented cube [Formula: see text], proposed by Choudum and Sunitha in 2002, is one of the most famous interconnection networks of the distributed parallel system. Reliability evaluation of underlying topological structures is vital for fault tolerance analysis of this system. As one of the most extensively studied parameters, the [Formula: see text]-conditional edge-connectivity of a connected graph [Formula: see text], [Formula: see text], is defined as the minimum number of the cardinality of the edge-cut of [Formula: see text], if exists, whose removal disconnects this graph and keeps each component of [Formula: see text] having minimum degree at least [Formula: see text]. Let [Formula: see text], [Formula: see text] and [Formula: see text] be three integers, where [Formula: see text], if [Formula: see text] and [Formula: see text], if [Formula: see text]. In this paper, we determine the exact value of the [Formula: see text]-conditional edge-connectivity of [Formula: see text], [Formula: see text] for each positive integer [Formula: see text] and [Formula: see text], and give an affirmative answer to Shinde and Borse’s corresponding conjecture on this topic in [On edge-fault tolerance in augmented cubes, J. Interconnection Netw. 20(4) (2020), DOI:10.1142/S0219265920500139].

scholarly journals Fault-Tolerance Distributed Control Plane for Software Defined Networks

2019 ◽  
Vol 26 (1) ◽  
pp. 101-121
Author(s):  
Vasily N. Pashkov
Keyword(s):  
Fault Tolerance ◽  
Distributed Control ◽  
High Availability ◽  
Software Defined Networks ◽  
Control Plane ◽  
Switch Control ◽  
Control Transfer ◽  
Minimum Number ◽  
Single Controller ◽  
Active Switch

The architecture of the high availability distributed control plane for SDN/OpenFlow networks are considered. High availability is achieved by redundancy of controller instances, active switch-controller communications, computing resources and tools for a controller instance failure and overloading detection and recovery. The proactive backup controller allocation algorithm which allows to minimize the time to repair in the case of a single controller instance failure is discussed. The algorithm for controller load-balancing allows dynamically reconfigure the control plane with a minimum number of switch control transfer operations to avoid controller instance overloading. The initial experimental results of the proposed algorithms for the HA distributed SDN control plane are described.

scholarly journals Fast Reliability Assessment of Neutral-Point-Clamped Topologies through Markov Models

2020 ◽  
Author(s):  
Sergio Busquets-Monge ◽  
Roya Rafiezadeh ◽  
Salvador Alepuz ◽  
Alber Filba-Martinez ◽  
Joan Nicolas-Apruzzese
Keyword(s):  
Fault Tolerance ◽  
Markov Models ◽  
Reliability Assessment ◽  
Open Circuit ◽  
Neutral Point ◽  
Time To Failure ◽  
Fast Calculation ◽  
Reliability Models ◽  
Minimum Number ◽  
Mean Time

This paper presents detailed Markov models for the reliability assessment of multilevel neutral-point-clamped (NPC) converter leg topologies, incorporating their inherent fault-tolerance under open-circuit switch faults. The Markov models are generated and discussed in detail for the three-level and four-level active NPC (ANPC) cases, while the presented methodology can be applied to easily generate the models for higher number of levels and for other topology variants. In addition, this paper also proposes an extremely fast calculation method to obtain the precise value of the system mean time to failure from any given formulated system Markov model. This method is then applied to quantitatively compare the reliability of two-level, three-level, and four-level ANPC legs under switch open-circuit-guaranteed faults and varying degrees of device paralleling. The comparison reveals that multilevel ANPC leg topologies inherently present a potential for a higher reliability than the conventional two-level leg, questioning the suitability of the traditional search for topologies with the minimum number of devices in order to improve reliability. Experimental results are presented to validate the fault-tolerance assumptions upon which the presented reliability models for the three-level and four-level ANPC legs are based.

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