Algorithm-Based Checkpoint-Recovery for the Conjugate Gradient Method

TL;DR

This paper introduces an algorithm-based checkpoint-recovery method called ESRP for the conjugate gradient solver, reducing overhead and improving resilience against node failures by exploiting algorithmic redundancies.

Contribution

The paper develops ESRP, a novel variant of ESR that minimizes data storage and recovery overhead, integrating checkpoint-restart concepts into the PCG solver.

Findings

ESRP reduces overhead compared to ESR and in-memory CR.

ESRP has lower overhead than CR in failure-free scenarios.

CR outperforms ESRP during node failures.

Abstract

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.