Fault Tolerance on Star Graphs

1997 ◽  
Vol 08 (02) ◽  
pp. 127-142 ◽  
Author(s):  
Shuo-Cheng Hu ◽  
Chang-Biau Yang
Keyword(s):  
Fault Tolerance ◽  
Fault Tolerant ◽  
Routing Algorithm ◽  
Constant Time ◽  
Multiprocessor Systems ◽  
Star Graph ◽  
Cycle Structure ◽  
Star Graphs ◽  
Broadcasting Algorithm

The capability of fault tolerance is one of the advantages of multiprocessor systems. In this paper, we prove that the fault tolerance of an n-star graph is 2n-5 with restriction to the forbidden faulty set. And we propose an algorithm for examining the connectivity of an n-star graph when there exist at most 2n - 4 faults. The algorithm requires O(n2 log n) time. Besides, we improve the fault-tolerant routing algorithm proposed by Bagherzadeh et al. by calculating the cycle structure of a permutation and the avoidance of routing message to a node without any nonfaulty neighbor. This calculation needs only constant time. And then, we propose an efficient fault-tolerant broadcasting algorithm. When there is no fault, our broadcasting algorithm remains optimal. The penalty is O(n) if there exists only one fault, and the penalty is O(n2) if there exist at most n - 2 faults.

ADAPTIVE FAULT-TOLERANT ROUTING IN STAR NETWORKS

2001 ◽  
Vol 02 (02) ◽  
pp. 213-231 ◽  
Author(s):  
KHALED DAY ◽  
ABDEL-ELAH AL-AYYOUB
Keyword(s):  
Minimum Distance ◽  
Fault Tolerant ◽  
Routing Algorithm ◽  
Star Graph ◽  
Node Failure ◽  
Star Network ◽  
Short Period ◽  
The Hierarchical Structure ◽  
Node Connectivity ◽  
Node Failures

We take advantage of the hierarchical structure of the star graph network to obtain an efficient method for constructing node-disjoint paths between arbitrary pairs of nodes in the network. A distributed fault-tolerant routing algorithm for the star network based on this construction method is then presented and evaluated. The proposed algorithm adapts the routing decisions in response to node failures. Node failure and repair conditions may arise dynamically (at any time) provided that the total number of faulty nodes at any given time is less than the node-connectivity n - 1 of the n-star. When a message is blocked due to faulty components, the source of the message is warned and requested to switch to a different node-disjoint path. The methods used to identify the paths, to propagate failure information back to source nodes, and to switch from a routing path to another incur little communication and computation overhead. We show that if the node failures occur 'reasonably' apart in time, then all messages will be routed on paths of length δ + ε where δ is the minimum distance between the source and the destination and ε is 0, 2, or 4. In the unlikely case where more failures occur in a 'short period', the algorithm still delivers all messages but via possibly longer paths.

FAULT-TOLERANT COMMUNICATIONS ON HYPERCUBE-CLUSTERS

2000 ◽  
Vol 01 (04) ◽  
pp. 315-329 ◽  
Author(s):  
PETER KOK KEONG LOH ◽  
WEN JING HSU
Keyword(s):  
Fault Tolerance ◽  
Interconnection Networks ◽  
Fault Tolerant ◽  
Routing Algorithm ◽  
Cost Effective ◽  
Hardware Support ◽  
Tolerance Level ◽  
Component Faults ◽  
Message Overhead ◽  
Standard Components

Hierarchical interconnection networks with n-dimensional hypercube clusters can strike a balance between wide application suitability, size scalability as well as reliability. Cluster communications support for such networks must therefore be reliable and efficient without incurring large overheads. This paper proposes a reliable and cost-effective intra-cluster communications strategy for such a class of interconnection networks. The routing algorithm can tolerate up to (n - 1) component faults in the cluster and generates routes that are cycle-free and livelock-free. The message is guaranteed to be optimally (respectively, sub-optimally) delivered within a maximum of n (respectively, 2n - 1) hops. The message overhead incurred is one of the lowest reported for the specified fault tolerance level – with only a single n-bit routing vector accompanying the message to be communicated. Finally, routing hardware support may be simply achieved with standard components, facilitating integration with the host network.

Double Stairs: A Fault-Tolerant Routing Algorithm for Networks-on-Chip

2016 ◽  
Vol 25 (06) ◽  
pp. 1650065 ◽  
Author(s):  
Saleh Fakhrali ◽  
Hamid R. Zarandi
Keyword(s):  
Fault Tolerance ◽  
Fault Tolerant ◽  
Routing Algorithm ◽  
Deep Submicron ◽  
Routing Algorithms ◽  
Experimental Results ◽  
Trade Off ◽  
Networks On Chip ◽  
On Chip ◽  
Probabilistic Flooding

Reliability is one of the main concerns in the design of networks-on-chip (NoCs) due to the use of deep submicron technologies in fabrication of such products. This paper presents a new fault-tolerant routing algorithm called double stairs for NoCs. Double stairs routing algorithm is a low overhead routing that has the ability to deal with fault. The proposed routing algorithm makes a redundant copy of each packet at the source node and routes the original and redundant packets in a new partially adaptive routing algorithm. The method is evaluated for various packet injection rates and fault rates. Experimental results show that the proposed routing algorithm offers the best trade-off between performance and fault tolerance compared to other routing algorithms, namely flooding, XYX and probabilistic flooding.

The Generalized Connectivity of Bubble-Sort Star Graphs

2019 ◽  
Vol 30 (05) ◽  
pp. 793-809
Author(s):  
Shu-Li Zhao ◽  
Rong-Xia Hao
Keyword(s):  
Fault Tolerance ◽  
Upper Bound ◽  
Interconnection Networks ◽  
Interconnection Network ◽  
Star Graph ◽  
Important Indicator ◽  
Star Graphs ◽  
Generalized Connectivity ◽  
Internally Disjoint Trees

The connectivity plays an important role in measuring the fault tolerance and reliability of interconnection networks. The generalized [Formula: see text]-connectivity of a graph [Formula: see text], denoted by [Formula: see text], is an important indicator of a network’s ability for fault tolerance and reliability. The bubble-sort star graph, denoted by [Formula: see text], is a well known interconnection network. In this paper, we show that [Formula: see text] for [Formula: see text], that is, for any three vertices in [Formula: see text], there exist [Formula: see text] internally disjoint trees connecting them in [Formula: see text] for [Formula: see text], which attains the upper bound of [Formula: see text] given by Li et al. for [Formula: see text].

Highly Fault-Tolerant Routing in the Star and Hypercube Interconnection Networks

1998 ◽  
Vol 08 (02) ◽  
pp. 221-230 ◽  
Author(s):  
A. A. Rescigno ◽  
U. Vaccaro
Keyword(s):  
Fault Tolerance ◽  
Interconnection Networks ◽  
Fault Tolerant ◽  
Minimal Length ◽  
Star Graph

The surviving route graph R(G, ρ)/F for a graph G, a routing ρ and a set of failures F is a graph consisting of all non-faulty vertices of G and with an edge between two vertices if there are no failures in the routing between the two vertices. Numerous papers have studied the diameter of R(G, ρ)/F as a measure of the fault-tolerance of G and ρ, assuming that the cardinality of F is strictly smaller than the connectivity of G. In this paper we study the diameter of R(G, ρ)/F, when G is either the n-star graph or the n-dimensional hypercube and ρ is any minimal length routing, under the assumption that F is any set of failures not containing all the neighbours of any vertex and |F| is at most twice the connectivity of G minus 3.

AN ADAPTIVE HEURISTIC ALGORITHM WITH THE PROBABILISTIC SAFETY VECTOR FOR FAULT-TOLERANT ROUTING ON THE (n, k)-STAR GRAPH

2014 ◽  
Vol 25 (06) ◽  
pp. 723-743 ◽  
Author(s):  
CHIAO-WEI CHIU ◽  
KUO-SI HUANG ◽  
CHANG-BIAU YANG ◽  
CHIOU-TING TSENG
Keyword(s):  
Fault Tolerant ◽  
Average Length ◽  
Routing Algorithm ◽  
Adaptive Method ◽  
Star Graph ◽  
Safety Level ◽  
Routing Performance ◽  
Preliminary Version ◽  
Adaptive Heuristic ◽  
Probabilistic Safety

The (n, k)-star graph is a generalization of the n-star graph. It has better scalability than the n-star graph and holds some good properties compared with the hypercube. This paper focuses on the design of the fault-tolerant routing algorithm for the (n, k)-star graph. We adopt the idea of collecting the limited global information used for routing on the n-star graph to the (n, k)-star graph. In the preliminary version of this paper, we built the probabilistic safety vector (PSV) with modified cycle patterns and developed the routing algorithm to decide the fault-free routing path with the help of PSV. Afterwards, we observed that the routing performance of PSV gets worse as the percentage of fault nodes increases, especially it exceeds 25%. In order to improve the routing performance with more faulty nodes, an adaptive method of threshold assignment for the PSV is also proposed. The performance is judged by the average length of routing paths. Compared with distance first search and safety level, PSV with dynamic threshold gets the best performance in the simulations.

FXY: A HIERARCHICAL ROUTING ALGORITHM TO BALANCE PERFORMANCE AND FAULT TOLERANCE IN NETWORKS-ON-CHIP

2014 ◽  
Vol 23 (10) ◽  
pp. 1450146 ◽  
Author(s):  
SALEH FAKHRALI ◽  
HAMID R. ZARANDI
Keyword(s):  
Fault Tolerance ◽  
Fault Tolerant ◽  
Routing Algorithm ◽  
Experimental Results ◽  
Balance Performance ◽  
Networks On Chip ◽  
Large Size ◽  
Trade Offs ◽  
And Performance ◽  
On Chip

This paper presents a hierarchical fault-tolerant routing algorithm called FXY, which is a hybrid method based on flooding and XY, and can balance performance and fault tolerance based on a predefined parameter m. First, FXY partitions the whole network into different equal size square submeshes with the size of m × m. At the first level of the hierarchy, packet routing within these submeshes is performed based on flooding routing algorithm. When the packets are received at effective boundary of each submesh, XY routing is performed to route the packet inter submeshes i.e., from one submesh to the neighbor submesh which is certainly one of its neighbor nodes. Here, the size of the submesh is defined as fault-tolerant granularity. As fault-tolerant granularity is increased, the size of the submeshes will be increased, therefore the method mainly floods packets in large-size submeshes and finally packets are received at their destinations correctly. On the other hand, when fault-tolerant granularity is decreased, the method mainly routes packets as XY method, which is not fault-tolerant, but has the best performance. The method is evaluated for various packet injection rates and fault rates. The experimental results reveal that the method presents a fault-tolerant routing algorithm, and can be adjusted so that it shows better fault-tolerance and performance trade-offs compared to XY and flooding which are two end-to-end cases of having the best performance and no fault-tolerance, having the least performance and the best fault tolerance, respectively. The experimental results for an 8 × 8 NoC size, have shown that 2-FXY, which is the proposed method with fault-tolerant granularity of two, offers the best trade-off between performance and fault tolerance compared to other methods, XY, flooding and probabilistic flooding.

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