arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2007.04066cs.DC
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共轭梯度法中基于递归的检查点恢复算法

Algorithm-Based Checkpoint-Recovery for the Conjugate Gradient Method

Carlos Pachajoa, Christina Pacher, Markus Levonyak, Wilfried N. Gansterer

摘要:

随着计算机达到亿亿次甚至更高的规模,故障的发生率将增加。解决这一问题是一个活跃的研究课题。我们专注于策略,使预处理共轭梯度(PCG)求解器弹性对节点故障,具体来说,精确的状态重建(ESR)方法,利用冗余PCG。降低冗余信息的存储频率可以减少运行时开销。然而,在节点故障之后,求解器必须从存储冗余信息的最后一次迭代重新启动,这增加了恢复开销。这个公式突出了该方法与检查点重启(CR)的相似之处。因此,这种方法,我们称之为ESR与周期性存储(ESRP),可以被认为是一种形式的基于算法的检查点重启。通过利用算法固有的冗余,而不是像CR中那样显式地存储状态。与CR相比,我们还最小化了要存储和检索的数据量,但需要额外的计算来重建求解器的状态。在本文中,我们描述了必要的修改ESR转换成ESRP,并进行了实验评估。我们比较ESRP实验与以前存在的ESR和应用级内存中的CR。我们的研究结果证实,ESR的开销显着减少,无论是在无故障的情况下,如果节点故障的介绍。在前一种情况下,ESRP的开销通常低于CR。但是,如果发生节点故障,CR会更快。我们声称,这些差异可以通过实施更适当的预条件来缓解。

英文摘要:

As computers reach exascale and beyond, the incidence of faults will increase. Solutions to this problem are an active research topic. We focus on strategies to make the preconditioned conjugate gradient (PCG) solver resilient against node failures, specifically, the exact state reconstruction (ESR) method, which exploits redundancies in PCG. Reducing the frequency at which redundant information is stored lessens the runtime overhead. However, after the node failure, the solver must restart from the last iteration for which redundant information was stored, which increases recovery overhead. This formulation highlights the method's similarities to checkpoint-restart (CR). Thus, this method, which we call ESR with periodic storage (ESRP), can be considered a form of algorithm-based checkpoint-restart. The state is stored implicitly, by exploiting redundancy inherent to the algorithm, rather than explicitly as in CR. We also minimize the amount of data to be stored and retrieved compared to CR, but additional computation is required to reconstruct the solver's state. In this paper, we describe the necessary modifications to ESR to convert it into ESRP, and perform an experimental evaluation. We compare ESRP experimentally with previously-existing ESR and application-level in-memory CR. Our results confirm that the overhead for ESR is reduced significantly, both in the failure-free case, and if node failures are introduced. In the former case, the overhead of ESRP is usually lower than that of CR. However, CR is faster if node failures happen. We claim that these differences can be alleviated by the implementation of more appropriate preconditioners.

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