Exploiting data representation for fault tolerance. Previous techniques for algorithm based fault tolerance abft 20 have been proposed for detecting errors in dense linear operations, but have high. The key idea of the abft technique is to encode the data at a higher level using checksum schemes and redesign algorithms to operate on the encoded data. Study on the efficiency and fault tolerance of block cipher algorithm based on energy analysis hao wang changchun university of science and technology abstract block cipher is one of the most widely used cryptographic systems. This article investigates the solution process for elliptic partial di erential equations that are discretized by nite elements. How to solve linear equations using a genetic algorithm. Linear programming algorithms linear programming definition. Formal methods, algebraic, model and process based specification, formal specification languages, refinement proofs, verification proofs, stampstpa techniques.
Now since this problem falls under the category of nphard problems i am looking for good local search based approaches to the problem. A linear algebraic model of algorithmbased fault tolerance, ieee trans. In fact, if you use a binary coded genetic algorithm then you wont be able to find the solution to the equations if your x, y can take negative values. Luk, a linear algebraic model of algorithmbased fault tolerance, ieee transactions on computers 37 12 1988 15991604. In the mathematics of quantum mechanics, a hamiltonian takes the form of a linear algebraic operator. Ive studied a variety of algorithms and taken a few linear algebra courses and i dont see the connection. In 1, 9, 10 a linear algebraic model of the weighted checksum scheme is developed, allowing parallels to be drawn between algorithm based fault tolerance and coding theory. A linear programming problem will have infinitely many solutions if and only if the last row to the left of the vertical line of the final simplex tableau has a zero in a column that is not a unit column.
The cause of these errors communication error, software error, etc. Abft into linear algebra matrix operations on gpus is a nontrivial task, which requires. Ieee transactions on cloud computing 1 a distributed secure. Algorithmic fault tolerance using the lanczos method. Soft error vulnerability of iterative linear algebra methods. The paper studies tuned implementations of the conventional a few parallel linear algebra method as examples on a generalized cmp model. In algorithm 1, dlartg and drotg are used together to firstly create the upper hessenberg matrix h, and then reduce it to upper triangular. The levenbergmarquardt algorithm does not handle bound constraints. We give the first nontrivial approximation algorithm for this problem, having an approximation guarantee of 3 h k, where k is the maximum requirement and h k is the kth harmonic number. A linear algebraic model of algorithmbased fault tolerance. Comparison of physical and softwareimplemented fault injection techniques. This is driving the interest in designing algorithms with builtin fault tolerance that can continue to operate and that can replace data even if part of the computation is lost in a failure. A linear algebraic model of algorithmbased fault tolerance abstract. Algorithmbased fault recovery of adaptively refined parallel.
This paper proposes a nonlinear model predictive control algorithm that is robust to bounded disturbances and tolerant to a finite number of faults. General linear codes for faulttolerant matrix operations on processor arrays, in proc. Solving systems of linear algebraic equations by monte carlo. Researchers have already proposed some algorithmbased fault tolerance abft techniques to overcome the problem of unreliable hardware by means of softwarealgorithm. A distributed algorithm based on multiagent network for. Research article, report by journal of applied mathematics. Self adapting linear algebra algorithms and software. Stealthy hardware trojan based algebraic fault analysis of. We consider a fault tolerant version of the metric facility location problem in which every city, j, is required to be connected to r j facilities. Algorithmic approaches to low overhead fault detection for. Index termsad hoc cloud, linear algebraic equations, outsourcing, distributed consensus, security, privacy. Towards a more fault resilient multigrid solver proceedings. Splice is an industrially developed and applied software architecture for.
For example what interesting things can one with a connectivity matrix for a graph. In the rst part we introduce our data allocation model and propose algorithms for optimizing the allocation. It is a conjugate gradient cg based algorithm for solving complex linear system. It is known to have the same computational power as a gatebased quantum computer. Towards practical algorithm based fault tolerance in dense linear algebra. A linear algebraic model of algorithmicbased fault. An overview of mathematical algorithms and software. Algorithmbased fault tolerance abft 20 was proposed to detect and correct errors in matrix multiplication operations. Nvp is used for providing faulttolerance in software. In linear system solving, is the choice between a direct. To detect errors during calculation result checking rc can be used. Researchers have already proposed some algorithm based fault tolerance abft techniques to overcome the problem of unreliable hardware by means of software algorithm.
A linear algebraic interpretation is developed for previously proposed algorithmbased fault tolerance schemes. Algorithm based fault tolerance for numerical linear. Example course topics might include things such as web operating systems, global file systems, distributed object based systems, fault tolerance distributed check pointing, highspeed networking, network security, active networking, group communication models, compilers for paralleldistributed computing, recent programming languages, and data. Parallel algorithms for dense linear algebra computations. Biser must be combined with linear algebra specific algorithm based fault tolerance. We present a performance model to compute the performance of. A realtime simulation has been performed in a vmebus environment utilizing a single board computer and a commercial realtime operating. In 29, the algorithm based fault tolerance abft is proposed to detect, locate. Numericaldefectcorrectionasan algorithmbasedfaulttolerance.
Our experimental comparison with softwarebased triple modular redundancy tmr clearly shows the runtime bene. Solving systems of linear algebraic equations by monte carlo method on regular arrays. In this type of search, a sequential search is made over all items one by one. Analog quantum computera quantum computer that carries out a computation without breaking the operations down to a small set of primitive operations gates on qubits. Steepness of the ascent from terascale to petascale to exascale. Efficient time complexity algorithm for linear programming problems. Jean arlat, yves crouzet, johan karlsson, peter folkesson, emmerich fuchs, and gunther h.
Study on the efficiency and fault tolerance of block cipher. This paper considers the problem of algorithmbased fault tolerance, and makes two major contributions. Mitra 2006, 2007, 2008 check pointing with stop and restart is not an option given the significant probability of soft errors and the o n2 lg n complexity of the threaded linear algebra routines. Faulttolerant niteelement multigrid algorithms with. The matrix in the lae is divided into submatrices by the columns. Study on the efficiency and fault tolerance of block. Mittal department of computer science and engineering, indian institute of technology, madras 600 036, india abstract the need for reliability of computers has been increasing, as computers have been put to use in more and more practical applications.
In algorithmbased fault tolerance abft, fault tolerance is tailored to the algorithm performed. A linear time algorithm for obtaining a twolayer wiring of w, if one exists, is devised. Software based protection algorithm based fault tolerance. Selfadapting linear algebra algorithms and software. Also, by increasing the area to at most 2a a twolayer wirable layout is obtained. The nvp is defined as the independent generation of functionally equivalent programs, called versions, from the same initial specification. Software design aspects for safety and fault tolerance. A realtime simulation has been performed in a vmebus environment utilizing a single board computer and a. The objective of the work presented in this paper was to use a formal model to. Several of my peers have mentioned that linear algebra is very important when studying algorithms. The linprog interiorpoint algorithm chooses the solution algorithm based on the density of columns. Although lots of methods are effective for fault diagnosis, it is hard to apply them to the case with tolerance influence. A linear algebraic model of algorithm based fault tolerance, ieee transactions on computers, vol. Fault tolerance in uniprocessor systems are usually handled by using time redundancy in the schedule so that any task instance can be reexecuted in presence of faults during the execution.
Example course topics might include things such as web operating systems, global file systems, distributed objectbased systems, fault tolerancedistributed check pointing, highspeed networking, network security, active networking, group communication models, compilers for paralleldistributed computing, recent programming languages, and data. Algorithm based fault tolerant and check pointing for high. If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Data structure and algorithms linear search tutorialspoint.
Distributed dense linear algebra on heterogeneous architectures. Thereby, the results are checked without knowledge of the particular algorithm used to calculate them. Algorithmbased fault tolerance for noncomputationally intensive applications. Algorithm based fault tolerance for numerical linear algebra on multicore processors. Mittal department of computer science and engineering, indian institute of technology, madras 600 036, india abstract the need for reliability of computers has been increasing, as computers have been. Soft error resilient qr factorization for hybrid system with. Algorithm based fault tolerance is studied for use with linear estimation algorithms such as the kalman filter. Traditionally, fault tolerance has been ignored in systems utilizing gpus because they were originally developed mainly for graphics applications, such as 3d games. The following results are established for an arbitrary verticaltwooverlap layout w with area a. Handing tolerance problem in fault diagnosis of linearanalogue circuits with accurate statistics approach. Abraham, a model for the analysis of fault tolerant signal processing architectures, proceedings of the international tech nology symposium spie, august, 1988, pp.
In this paper, a robust statistics based approach is introduced for tolerance influencing fault diagnosis. This method is pay as you go, meaning that there is practically only a runtime overhead if errors occur and a correction is performed. We investigate basic properties of the algebraic solutions to the interval linear systems and propose a. Pdf algorithmbased fault tolerance for failstop failures. To highlight the characteristics of aerospace models, generic nonlinear dynamical mode. As the deployment of the gpgpus grows rapidly, fault tolerance that has traditionally been relegated to only cpu based computing systems, started to emerge on gpu based platforms. A linear programming problem will have no solution if the simplex method breaks down at some stage. An algebraic specification for ctl with time constraints. It has been proved in the previous algorithmbased fault tolerance research.
Soft error vulnerability of iterative linear algebra. The quantum algorithm for linear systems of equations, designed by aram harrow, avinatan hassidim, and seth lloyd, is a quantum algorithm formulated in 2009 for solving linear systems. Basic fault tolerant software techniques geeksforgeeks. In this paper, we elaborate an algebraic fault analysis of hight with a stealthy ht. Practice using one or more of these software tools on. The algorithm estimates the result of a scalar measurement on the solution vector to a given linear system of equations. Handing tolerance problem in fault diagnosis of linear. F 1 introduction c loud computing is a revolutionary paradigm of delivering network resources, ranging from computational power and data storage to platform and software, as a service over the network 1. An analysis of algorithmbased fault tolerance techniques.
Selfadapting linear algebra algorithms and software james demmel, fellow, ieee, jack dongarra, fellow. Algorithmbased fault tolerance abft, originally developed by. Circuit printing engineering research fault location engineering printed circuit boards printed circuits. Algorithmbased fault tolerance for matrix operations on gpgpus. Proceedings of spie january 04 1986 faulttolerant qr decomposition for adaptive signal processing proceedings of spie october 28 1994 a novel fault tolerance technique for recursive least squares minimization proceedings of spie february 23 1988 choosing. The concepts of distance, code space, and the definitions of detection and correction in the vector space rsup n are clarified. Handing tolerance problem in fault diagnosis of linear analogue circuits with accurate statistics approach. Emphasis is placed on the study of algorithm based fault tolerance used in conjunction with the udu t covariance calculation. Algorithm based fault tolerance abft is a costeffective technique for improving the reliability of a multiprocessor system. Design and analysis of algorithmbased fault tolerant. A linear algebraic model of algorithm based fault tolerance, ieee transactions on. Every item is checked and if a match is found then that particular item is returned, otherwise the search continues till the end of the data collection. For linear algebra kernels, another widely used technique for silent error. Algorithm based fault tolerance abft attracts renewed interest for its extremely low overhead and good scalability.
Analysis and randomized design of algorithmbased fault tolerant multiprocessor systems under the extended graphtheoretic model, in proc. Algorithm based fault tolerance abft has been suggested as a. A lot of people suggests strassens algorithm but it has a very big hidden constant which makes it inefficient. Ieee transactions on cloud computing 1 a distributed. First, it shows how very general sequences of polynomials can be used to generate the checksums, so as to reduce the chance of numerical overflows. Wasp based algorithms and applications dana simian.
Either you can code the whole genetic algorithm yourself, or you can just use a good existing rga code to solve your problem. Towards practical algorithm based fault tolerance in dense linear. Fault tolerance techniques for highperformance computing. In the second part we present proofofconcept numerical experiments with a wavelet discretization of a simple di erential equation. We examine novel fault tolerance schemes for data loss in multigrid solvers which essentially combine ideas of checkpointrestart with algorithmbased fault tolerance. Tolerating silent data corruption in opaque preconditioners. Soft error resilient qr factorization for hybrid system. Based on i software as a service i computing centers providing ressources in a pay as. Softwarehardware techniques to reduce checkpoint, recovery. A novel linear algebraic interpretation is developed for previously proposed algorithmbased faulttolerance schemes. Common in the fused operation are the following two operation steps.
A new and faster gaussian elimination based fault tolerant systolic linear system solver. The concepts of distance, code space, and the definitions of detection and correction in the vector space rsup n are explained. Algorithmbased fault recovery of adaptively refined. Previous techniques for algorithm based fault tolerance abft 20 have been proposed for detecting errors in dense linear operations, but have high overhead in the context of sparse problems.
As parallel and distributed systems scale, fault tolerance is an increasingly important problem particularly on systems with limited io capacity and bandwidth. We support both linear algebraic operations of between two dense matrices, and between sparse and dense matrices in distributed environments. Algorithmbased fault tolerance for matrix operations ieee xplore. The program executes on n processors, there is a single check pointing processor. Faulttolerant computing, silent errors, algorithmbased fault tolerance. A survey of parallel algorithms in numerical linear algebra. After calculating the corrected newton step, the algorithm performs more calculations to get both a longer current step, and to prepare.
A layout model called verticaltwooverlap is introduced. Numerical defect correction as an algorithmbased fault. In 14, a general faulttolerant synthesis scheme for linear operations is proposed. Courses university of kentucky college of engineering. As the fault model is the deciding factor in choosing an effective checksum. Analog signala signal whose value varies smoothly within a range of real or complex numbers. Circuit printing engineering research fault location. The rapid progress in vlsi technology has reduced the cost of hardware, allowing multiple copies of lowcost processors to provide a large amount of comput.
It has more recently been generalized 2 and extended to more general linear algebra algorithms. Index terms algorithmbased fault tolerance, defect correction, conjugated gradient, triple modular redundancy, check. Using one of these factorizations, namely lu with partial pivoting, which is signi. To highlight the characteristics of aerospace models, generic nonlinear dynamical modelling from flight mechanics is recalled and a unifying representation of sensor and actuator faults is presented. The fourth contribution of this manuscript is a software based on ftmpi. Fault tolerance in real time systems scheduling summary. Quantum algorithm for linear systems of equations wikipedia. Algorithmbased fault tolerance abft, originally developed by huang and abraham, is a lowcost fault tolerance scheme to detect and correct permanent and transient errors in certain matrix operations on systolic arrays. Fault resilience of the algebraic multigrid solver.
In the widely used parallel numerical linear algebra library. Faults that occur in the parallel geometric multigrid solver are studied in various model scenarios. This model enables the algorithm to tolerate a certain set of multiple failures. In comparison, algorithmbased fault tolerance abft is a promising fault tolerance method with low recovery overhead, but it suffers from the inadequacy of universal applicability, i. This paper considers the problem of algorithm based fault tolerance, and makes two major contributions. In this talk, we will firstly show the novel concept of erasure coded computations, which augments a given. This paper presents a distributed discretetime consensus algorithm based on multiagent network to solve largescale linear algebraic equation lae. An approximation algorithm for the fault tolerant metric. For fault free computations, the use of adaptive refinement techniques in combination with finite element methods is well established. The tolerance handling in analogue fault diagnosis is a challenging problem. In linear system solving, is the choice between a direct and an iterative method free or are there. Elsevier microprocessors and microsystems 21 1997 151161 microcessors and microsystems algorithmbased fault tolerance.
In the underdetermined case, lsqcurvefit uses the levenbergmarquardt algorithm. To improve e ciency compared to conventional global checkpointing, we exploit the inherent data compression of the multigrid hierarchy, and relax the. Pdf faulttolerant tubebased robust nonlinear model. Algorithm based fault tolerant synthesis for linear operations. Provide an overview of fastmath software tools available to perform these tasks on hpc architectures. In comparison, algorithm based fault tolerance abft is a promising fault tolerance method with low recovery overhead, but it suffers from the inadequacy of universal applicability, i.
Transient error detection during udut covariance calculations. In concept, the nvp scheme is similar to the nmodular redundancy scheme used to provide tolerance against hardware faults. The advantage of this proposed method is that it can accurately locate the data fusion. This survey of model based fault diagnosis focuses on those methods that are applicable to aerospace systems. A faster algorithm for solving linear algebraic equations on the star graph. Algorithmbased fault tolerance abft is a costeffective technique for improving the reliability of a multiprocessor system. Solve nonlinear curvefitting datafitting problems in. It is a kind of symmetric cipher algorithm, which uses the same key for en cryption and decryption. Abstractwe demonstrate algorithmbased fault tolerance for silent, transient data corruption in blackbox preconditioners. The fault model we choose in this attack is the one in which the adversary is assumed to inject a singlebit fault precisely in both location and the time of the disturbance by a ht which is activated just by choosing certain plaintexts. An rc for matrixmatrix multiplication c ab with input. Hence you need to use a real coded genetic algorithm.
Exploiting data representation for fault tolerance request pdf. Software and algorithmbased fault tolerance measures operate on top of the hard. The effectiveness of sparse, linear solvers is typically studied in terms of their convergence properties and computational complexity, while their ability to handle transient hardware errors, such as bitflips that lead to silent data corruption sdc, has received less attention. There has been prior work on checksumbased algorithmic approaches to faulttolerance of linear algebrabased applications. The trustregionreflective algorithm does not solve underdetermined systems. We consider both additive schwarz domain decomposition with an iluk subdomain solver, and algebraic multigrid, both implemented in the trilinos library. Checkpoint and recovery cost imposed by checkpointrestart cpr is a crucial performance issue for highperformance computing hpc applications.
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