Improving Performance of Iterative Methods by Lossy Checkponting

Iterative methods are commonly used approaches to solve large, sparse linear systems, which are fundamental operations for many modern scientific simulations. When the large-scale iterative methods are running with a large number of ranks in parallel, they have to checkpoint the dynamic variables periodically in case of unavoidable fail-stop errors, requiring fast I/O systems and large storage space. To this end, significantly reducing the checkpointing overhead is critical to improving the overall performance of iterative methods. Our contribution is fourfold. (1) We propose a novel lossy checkpointing scheme that can significantly improve the checkpointing performance of iterative methods by leveraging lossy compressors. (2) We formulate a lossy checkpointing performance model and derive theoretically an upper bound for the extra number of iterations caused by the distortion of data in lossy checkpoints, in order to guarantee the performance improvement under the lossy checkpointing scheme. (3) We analyze the impact of lossy checkpointing (i.e., extra number of iterations caused by lossy checkpointing files) for multiple types of iterative methods. (4)We evaluate the lossy checkpointing scheme with optimal checkpointing intervals on a high-performance computing environment with 2,048 cores, using a well-known scientific computation package PETSc and a state-of-the-art checkpoint/restart toolkit. Experiments show that our optimized lossy checkpointing scheme can significantly reduce the fault tolerance overhead for iterative methods by 23%~70% compared with traditional checkpointing and 20%~58% compared with lossless-compressed checkpointing, in the presence of system failures.Comment: 14 pages, 10 figures, HPDC'1

Robust Algorithms for the Secretary Problem

In classical secretary problems, a sequence of n elements arrive in a uniformly random order, and we want to choose a single item, or a set of size K. The random order model allows us to escape from the strong lower bounds for the adversarial order setting, and excellent algorithms are known in this setting. However, one worrying aspect of these results is that the algorithms overfit to the model: they are not very robust. Indeed, if a few "outlier" arrivals are adversarially placed in the arrival sequence, the algorithms perform poorly. E.g., Dynkin’s popular 1/e-secretary algorithm is sensitive to even a single adversarial arrival: if the adversary gives one large bid at the beginning of the stream, the algorithm does not select any element at all. We investigate a robust version of the secretary problem. In the Byzantine Secretary model, we have two kinds of elements: green (good) and red (rogue). The values of all elements are chosen by the adversary. The green elements arrive at times uniformly randomly drawn from [0,1]. The red elements, however, arrive at adversarially chosen times. Naturally, the algorithm does not see these colors: how well can it solve secretary problems? We show that selecting the highest value red set, or the single largest green element is not possible with even a small fraction of red items. However, on the positive side, we show that these are the only bad cases, by giving algorithms which get value comparable to the value of the optimal green set minus the largest green item. (This benchmark reminds us of regret minimization and digital auctions, where we subtract an additive term depending on the "scale" of the problem.) Specifically, we give an algorithm to pick K elements, which gets within (1-ε) factor of the above benchmark, as long as K ≥ poly(ε^{-1} log n). We extend this to the knapsack secretary problem, for large knapsack size K. For the single-item case, an analogous benchmark is the value of the second-largest green item. For value-maximization, we give a poly log^* n-competitive algorithm, using a multi-layered bucketing scheme that adaptively refines our estimates of second-max over time. For probability-maximization, we show the existence of a good randomized algorithm, using the minimax principle. We hope that this work will spur further research on robust algorithms for the secretary problem, and for other problems in sequential decision-making, where the existing algorithms are not robust and often tend to overfit to the model.ISSN:1868-896

Checkpointing of parallel applications in a Grid environment

The Grid environment is generic, heterogeneous, and dynamic with lots of unreliable resources making it very exposed to failures. The environment is unreliable because it is geographically dispersed involving multiple autonomous administrative domains and it is composed of a large number of components. Examples of failures in the Grid environment can be: application crash, Grid node crash, network failures, and Grid system component failures. These types of failures can affect the execution of parallel/distributed application in the Grid environment and so, protections against these faults are crucial. Therefore, it is essential to develop efficient fault tolerant mechanisms to allow users to successfully execute Grid applications. One of the research challenges in Grid computing is to be able to develop a fault tolerant solution that will ensure Grid applications are executed reliably with minimum overhead incurred. While checkpointing is the most common method to achieve fault tolerance, there is still a lot of work to be done to improve the efficiency of the mechanism. This thesis provides an in-depth description of a novel solution for checkpointing parallel applications executed on a Grid. The checkpointing mechanism implemented allows to checkpoint an application at regions where there is no interprocess communication involved and therefore reducing the checkpointing overhead and checkpoint size

Integrating Scale Out and Fault Tolerance in Stream Processing using Operator State Management

As users of big data applications expect fresh results, we witness a new breed of stream processing systems (SPS) that are designed to scale to large numbers of cloud-hosted machines. Such systems face new challenges: (i) to benefit from the pay-as-you-go model of cloud computing, they must scale out on demand, acquiring additional virtual machines (VMs) and parallelising operators when the workload increases; (ii) failures are common with deployments on hundreds of VMs - systems must be fault-tolerant with fast recovery times, yet low per-machine overheads. An open question is how to achieve these two goals when stream queries include stateful operators, which must be scaled out and recovered without affecting query results. Our key idea is to expose internal operator state explicitly to the SPS through a set of state management primitives. Based on them, we describe an integrated approach for dynamic scale out and recovery of stateful operators. Externalised operator state is checkpointed periodically by the SPS and backed up to upstream VMs. The SPS identifies individual operator bottlenecks and automatically scales them out by allocating new VMs and partitioning the check-pointed state. At any point, failed operators are recovered by restoring checkpointed state on a new VM and replaying unprocessed tuples. We evaluate this approach with the Linear Road Benchmark on the Amazon EC2 cloud platform and show that it can scale automatically to a load factor of L=350 with 50 VMs, while recovering quickly from failures. Copyright © 2013 ACM

Heterogeneity aware fault tolerance for extreme scale computing

Upcoming Extreme Scale, or Exascale, Computing Systems are expected to deliver a peak performance of at least 10^18 floating point operations per second (FLOPS), primarily through significant expansion in scale. A major concern for such large scale systems, however, is how to deal with failures in the system. This is because the impact of failures on system efficiency, while utilizing existing fault tolerance techniques, generally also increases with scale. Hence, current research effort in this area has been directed at optimizing various aspects of fault tolerance techniques to reduce their overhead at scale. One characteristic that has been overlooked so far, however, is heterogeneity, specifically in the rate at which individual components of the underlying system fail, and in the execution profile of a parallel application running on such a system. In this thesis, we investigate the implications of such types of heterogeneity for fault tolerance in large scale high performance computing (HPC) systems. To that end, we 1) study how knowledge of heterogeneity in system failure likelihoods can be utilized to make current fault tolerance schemes more efficient, 2) assess the feasibility of utilizing application imbalance for improved fault tolerance at scale, and 3) propose and evaluate changes to system level resource managers in order to achieve reliable job placement over resources with unequal failure likelihoods. The results in this thesis, taken together, demonstrate that heterogeneity in failure likelihoods significantly changes the landscape of fault tolerance for large scale HPC systems

Toward an Optimal Online Checkpoint Solution under a Two-Level HPC Checkpoint Model

The traditional single-level checkpointing method suffers from significantoverhead on large-scale platforms. Hence, multilevel checkpointing protocols have been studied extensively in recent years. The multilevel checkpoint approach allows different levels of checkpoints to be set (each with different checkpoint overheads and recovery abilities), in order to further improve the fault tolerance performance of extreme-scale HPC applications. How to optimize the checkpoint intervals for each level, however, is an extremely difficult problem. In this paper, we construct an easy-to-use two-level checkpoint model. Checkpoint level 1 deals with errors with low checkpoint/recovery overheads such as transient memory errors, while checkpoint level 2 deals with hardware crashes such as node failures.Compared with previous optimization work, our new optimal checkpoint solution offers two improvements: (1) it is an online solution without requiring knowledge of the job length in advance, and (2) it shows that periodic patterns are optimal and determines the best pattern. We evaluate the proposed solution and compare it with the most up-to-date related approaches on an extreme-scale simulation testbed constructed based on a real HPC application execution. Simulation results show that our proposed solution outperforms other optimized solutions and can improve the performance significantly in some cases. Specifically, with the new solution the wall-clock time can be reduced by up to 25.3\% over that of other state-of-the-art approaches. Finally, a brute-force comparison with all possible patterns shows that our solution is always within $1\%$ of the best pattern in the experiments

Program Reversal Schedules for Single- and Multi-processor Machines

Bei der Berechnung von Adjungierten, zum Debuggen und für ähnliche Anwendungen kann man die Umkehr der entsprechenden Programmauswertung verwenden. Der einfachste Ansatz, nämlich das Mitschreiben einer kompletten Mitschrift der Vorwärtsrechnung, welche anschließend rückwärts gelesen wird, verursacht einen enormen Speicherplatzbedarf. Als Alternative dazu kann man die Mitschrift auch stückweise erzeugen, indem die Programmauswertung von passend gewählten Checkpoints wiederholt gestartet wird. Das Ziel der Arbeit ist die Minimierung des von der Programmumkehr verursachten Zeit- und Speicherplatzbedarfs. Dieser wird gemessen in Auswertungswiederholungen bzw. verwendeten Checkpoints. Optimale Umkehrschemata werden für Ein- und Mehr-Schritt-Verfahren entwickelt, welche zum Beispiel bei der Diskretisierung einer gewöhnlichen Differentialgleichung Verwendung finden. Desweiteren erfolgte die Entwicklung von parallelen Umkehrschemata, d. h. mehrere Prozessoren werden für die Umkehrung der Programmauswertung eingesetzt. Diese zusätzlichen Prozessoren dienen dazu, die wiederholten Berechnungen des Programms zu parallelisieren, so daß ein Prozessor die Rückwartsrechnung ohne Unterbrechung durchführen kann. Sowohl für die seriellen als auch für die parallelen Umkehrschemata wurde gezeigt, daß die Länge der umzukehrenden Programmauswertung exponentiell in Abhängigkeit von der Zahl der verwendeten Checkpoints und der Zahl der wiederholten Auswertungen bzw. verwendeten Prozessoren wächst.For adjoint calculations, parameter estimation, and similar purposes one may need to reverse the execution of a computer program. The simplest option is to record a complete execution log and then to read it backwards. This requires massive amounts of storage. Instead one may generate the execution log piecewise by restarting the ``forward'' calculation repeatedly from suitably placed checkpoints. The basic structure of the resulting reversal schedules is illustrated. Various strategies are analysed with respect to the resulting temporal and spatial complexity on serial and parallel machines. For serial machines known optimal compromises between operations count and memory requirement are explained, and they are extended to more general situations. For program execution reversal on multi-processors the new challenges and demands on an optimal reversal schedule are described. We present parallel reversal schedules that are provably optimal with regards to the number of concurrent processes and the total amount of memory required

On the impact of process replication on executions of large-scale parallel applications with coordinated checkpointing

International audienceProcessor failures in post-petascale parallel computing platforms are common occurrences. The traditional fault-tolerance solution, checkpoint-rollback-recovery, severely limits parallel efficiency. One solution is to replicate application processes so that a processor failure does not necessarily imply an application failure. Process replication, combined with checkpoint-rollback-recovery, has been recently advocated. We first derive novel theoretical results for Exponential failure distributions, namely exact values for the Mean Number of Failures To Interruption and the Mean Time To Interruption. We then extend these results to arbitrary failure distributions, obtaining closed-form solutions for Weibull distributions. Finally, we evaluate process replica-tion in simulation using both synthetic and real-world failure traces so as to quantify average application makespan. One interesting result from these experiments is that, when process repli-cation is used, application performance is not sensitive to the checkpointing period, provided that that period is within a large neighborhood of the optimal period. More generally, our empirical results make it possible to identify regimes in which process replication is beneficial