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On the Fault Tolerance of Some Popular BoundedDegree Networks
 SIAM Journal on Computing
, 1992
"... In this paper, we analyze the ability of several boundeddegree networks that are commonly used for parallel computation to tolerate faults. Among other things, we show that an Nnode butterfly containing N 1\Gammaffl worstcase faults (for any constant ffl ? 0) can emulate a faultfree butterfly ..."
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Cited by 49 (9 self)
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In this paper, we analyze the ability of several boundeddegree networks that are commonly used for parallel computation to tolerate faults. Among other things, we show that an Nnode butterfly containing N 1\Gammaffl worstcase faults (for any constant ffl ? 0) can emulate a faultfree butterfly of the same size with only constant slowdown. Similar results are proved for the shuffleexchange graph. Hence, these networks become the first connected boundeddegree networks known to be able to sustain more than a constant number of worstcase faults without suffering more than a constantfactor slowdown in performance. We also show that an Nnode butterfly whose nodes fail with some constant probability p can emulate a faultfree version of itself with a slowdown of 2 O(log N) , which is a very slowly increasing function of N . The proofs of these results combine the technique of redundant computation with new algorithms for (packet) routing around faults in hypercubic networks. Tech...
Fault Tolerant Networks With Small Degree
 In Proceedings of the 12th ACM Symposium on Parallel Algorithms and Architectures (SPAA
, 2000
"... In this paper, we study the design of fault tolerant networks for arrays and meshes by adding redundant nodes and edges. For a target graph G (linear array or mesh in this paper), a graph G # is called a kfaulttolerant graph of G if when we remove any k nodes from G # , it still contains a subg ..."
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Cited by 15 (0 self)
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In this paper, we study the design of fault tolerant networks for arrays and meshes by adding redundant nodes and edges. For a target graph G (linear array or mesh in this paper), a graph G # is called a kfaulttolerant graph of G if when we remove any k nodes from G # , it still contains a subgraph isomorphic to G. The major quality measures for a faulttolerant graph are the number of spare nodes it uses and the maximum degree it has. The degree is particularly important in practice as it poses constraints on the scalability of the system. In this paper, we aim at designing faulttolerant graphs with both small degree and small number of spare nodes. The graphs we obtain have degree O(1) for arrays and O(log 3 k) for meshes. The number of spare nodes used are O(k log 2 k) and O(k 2 / log k), respectively. Compared to the previous results, the number of spare nodes used in our construction has one fewer linear factor in k. 1 1 Introduction In many parallel computer ...
Reconfiguring Arrays with Faults Part I: WorstCase Faults
 SIAM Journal on Computing
, 1997
"... . In this paper we study the ability of arraybased networks to tolerate worstcase faults. We show that an N \Theta N twodimensional array can sustain N 1\Gammaffl worstcase faults, for any fixed ffl ? 0, and still emulate T steps of a fully functioning N \Theta N array in O(T +N) steps, i.e., ..."
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Cited by 13 (1 self)
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. In this paper we study the ability of arraybased networks to tolerate worstcase faults. We show that an N \Theta N twodimensional array can sustain N 1\Gammaffl worstcase faults, for any fixed ffl ? 0, and still emulate T steps of a fully functioning N \Theta N array in O(T +N) steps, i.e., with only constant slowdown. Previously it was known only that an array could tolerate a constant number of faults with constant slowdown. We also show that if faulty nodes are allowed to communicate, but not compute, then an Nnode onedimensional array can tolerate log k N worstcase faults, for any constant k ? 0, and still emulate a faultfree array with constant slowdown, and this bound is tight. Key words. fault tolerance, arraybased network, mesh network, network emulation AMS subject classifications. 68M07, 68M10, 68M15, 68Q68 1. Introduction. In a truly large parallel computer, some components are bound to fail. Knowing this, a programmer can write software that explicitly cope...
Designing and Embedding Reliable Virtual Infrastructures.
, 2010
"... ABSTRACT In a virtualized infrastructure where physical resources are shared, a single physical server failure will terminate several virtual servers and crippling the virtual infrastructures which contained those virtual servers. In the worst case, more failures may cascade from overloading the re ..."
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Cited by 9 (3 self)
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ABSTRACT In a virtualized infrastructure where physical resources are shared, a single physical server failure will terminate several virtual servers and crippling the virtual infrastructures which contained those virtual servers. In the worst case, more failures may cascade from overloading the remaining servers. To guarantee some level of reliability, each virtual infrastructure, at instantiation, should be augmented with backup virtual nodes and links that have sufficient capacities. This ensures that, when physical failures occur, sufficient computing resources are available and the virtual network topology is preserved. However, in doing so, the utilization of the physical infrastructure may be greatly reduced. This can be circumvented if backup resources are pooled and shared across multiple virtual infrastructures, and intelligently embedded in the physical infrastructure. These techniques can reduce the physical footprint of virtual backups while guaranteeing reliability.
Reliability Support in Virtual Infrastructures
, 2010
"... Through the recent emergence of joint resource and network virtualization, dynamic composition and provisioning of timelimited and isolated virtual infrastructures is now possible. One other benefit of infrastructure virtualization is the capability of transparent reliability provisioning (reliabil ..."
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Cited by 3 (1 self)
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Through the recent emergence of joint resource and network virtualization, dynamic composition and provisioning of timelimited and isolated virtual infrastructures is now possible. One other benefit of infrastructure virtualization is the capability of transparent reliability provisioning (reliability becomes a service provided by the infrastructure). In this context, we discuss the motivations and gains of introducing customizable reliability of virtual infrastructures when executing largescale distributed applications, and present a framework to specify, allocate and deploy virtualized infrastructure with reliability capabilities. An approach to efficiently specify and control the reliability at runtime is proposed. We illustrate these ideas by analyzing the introduction of reliability at the virtualinfrastructure level on a real application. Experimental results, obtained with an actual medicalimaging application running in virtual infrastructures provisioned in the experimental largescale Grid’5000 platform, show the benefits of the virtualization of reliability.
Explicit Constructions of Fault Tolerant Open Linear Arrays
, 2005
"... Two graph models for a Kfault tolerant linear array with external inputs and outputs are proposed: one is with minimum number of spare nodes and incurs low spare resource overhead, and the other is with small internal degree and incurs small runtime reconfiguration hardware overhead. Both graph mo ..."
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Cited by 2 (0 self)
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Two graph models for a Kfault tolerant linear array with external inputs and outputs are proposed: one is with minimum number of spare nodes and incurs low spare resource overhead, and the other is with small internal degree and incurs small runtime reconfiguration hardware overhead. Both graph models can be applied to fault tolerant VLSI designs while maintaining low hardware cost.
Fault Tolerant Asynchronous Adder through Dynamic Selfreconfiguration
"... This paper presents a systematic method for the design of a reconfigurable selfhealing asynchronous adder. We propose a graphbased model for the design of a faulttolerant linear array with external inputs and outputs with a minimum number of spare resources. A Kfaulttolerant asynchronous adder ..."
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This paper presents a systematic method for the design of a reconfigurable selfhealing asynchronous adder. We propose a graphbased model for the design of a faulttolerant linear array with external inputs and outputs with a minimum number of spare resources. A Kfaulttolerant asynchronous adder design is presented based on this analysis, together with the necessary support logic for dynamic selfreconfiguration. Experimental evaluations show that our method incurs both low hardware cost and small performance overhead compared to traditional approaches to faulttolerance. 1
Fault Tolerant Asynchronous Adder through Dynamic Selfreconfiguration
"... This paper presents a systematic method for the design of a selfhealing asynchronous adder. We propose a graphbased model for the design of a faulttolerant linear array with external inputs and outputs with a minimum number of spare resources. A Kfaulttolerant asynchronous adder design is presen ..."
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This paper presents a systematic method for the design of a selfhealing asynchronous adder. We propose a graphbased model for the design of a faulttolerant linear array with external inputs and outputs with a minimum number of spare resources. A Kfaulttolerant asynchronous adder design is presented based on this analysis, together with the necessary support logic for dynamic selfreconfiguration. Experimental evaluations show that our method incurs both low hardware cost and small performance overhead compared to traditional approaches to faulttolerance. 1
Universality, tolerance, chaos and order
, 2010
"... What is the minimum possible number of edges in a graph that contains a copy of every graph on n vertices with maximum degree a most k? This question, as well as several related variants, received a considerable amount of attention during the last decade. In this short survey we describe the known r ..."
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What is the minimum possible number of edges in a graph that contains a copy of every graph on n vertices with maximum degree a most k? This question, as well as several related variants, received a considerable amount of attention during the last decade. In this short survey we describe the known results focusing on the main ideas in the proofs, discuss the remaining open problems, and mention a recent application in the investigation of the complexity of subgraph containment problems.
FaultTolerant Hypercubes with Small Degree
"... For a given Nvertex graph. H, a graph G obtained from H by adding t vertices a,nd some edges is called a tFT (tfaulttoleran,t) graph. for H if even after deletin.g any t vertices from G, the remaining graph contains H as a subgraph. For an Nvertex hypercube QN, a tFT graph with an, optimal n ..."
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For a given Nvertex graph. H, a graph G obtained from H by adding t vertices a,nd some edges is called a tFT (tfaulttoleran,t) graph. for H if even after deletin.g any t vertices from G, the remaining graph contains H as a subgraph. For an Nvertex hypercube QN, a tFT graph with an, optimal number O(tN +t2) of added edges and maximum degree of O(N + t), and a, tFT graph zuith O(tN log N) added edges and maximum degree of O(t 1ogN) have been known. In this paper, we introduce some tFT graphs for QN with an optimal number O(tN + t2) of added edges and small maximum degree. In particular, we show a tFT graph, for QN with 2ctN+ct2 v ’ added edges and max c> imum degree of 0 (,0g~~2 N) + 4ct 1