论文标题

通过相对性能区分等效算法

Discriminating Equivalent Algorithms via Relative Performance

论文作者

Sankaran, Aravind, Bientinesi, Paolo

论文摘要

在科学计算中,通常可以通过许多不同的算法(有时超过数百个)来计算数学表达式,每个算法都可以识别特定的库调用序列。尽管在数学上等效,但这些算法在性能方面可能表现出显着差异。但是,实际上,由于波动,没有一种算法始终如一地表现出色。因此,通过这项工作,我们旨在确定最佳算法,而是算法的子集,这些算法比其他算法要快。为此,我们没有使用以绝对术语来量化算法的性能的常规方法,而是提出了一种基于测量的聚类方法,将算法分类为等效性(或性能)类,使用成对的比较。我们表明,基于相对性能,即使在嘈杂的系统条件下,这种方法也会导致对最快算法的强大识别。此外,它可以开发用于自动算法选择的实用机器学习模型。

In scientific computing, it is common that a mathematical expression can be computed by many different algorithms (sometimes over hundreds), each identifying a specific sequence of library calls. Although mathematically equivalent, those algorithms might exhibit significant differences in terms of performance. However in practice, due to fluctuations, there is not one algorithm that consistently performs noticeably better than the rest. For this reason, with this work we aim to identify not the one best algorithm, but the subset of algorithms that are reliably faster than the rest. To this end, instead of using the usual approach of quantifying the performance of an algorithm in absolute terms, we present a measurement-based clustering approach to sort the algorithms into equivalence (or performance) classes using pair-wise comparisons. We show that this approach, based on relative performance, leads to robust identification of the fastest algorithms even under noisy system conditions. Furthermore, it enables the development of practical machine learning models for automatic algorithm selection.

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