Coded computing has emerged as a key framework for addressing the impact of stragglers in distributed computation. While polynomial functions often admit exact recovery under existing coded computing schemes, non-polynomial functions require approximate reconstruction from a finite number of evaluations, posing significant challenges. Consequently, interpolation-based methods for non-polynomial coded computing have gained attention, with Berrut approximated coded computing emerging as a state-of-the-art approach. However, due to the global support of Berrut interpolants, the reconstruction accuracy degrades significantly as the number of stragglers increases. To address this challenge, we propose a coded computing framework based on cubic B-spline interpolation. In our approach, server-side function evaluations are reconstructed at the master using B-splines, exploiting their local support and smoothness properties to enhance stability and accuracy. We provide a systematic methodology for integrating B-spline interpolation into coded computing and derive theoretical bounds on approximation error for certain class of smooth functions. Our analysis demonstrates that the error bounds of our approach exhibit a faster decay with respect to the number of workers compared to the Berrut-based method. Experimental results also confirm that our method offers improved accuracy over Berrut-based methods for various smooth non-polynomial functions.

翻译：编码计算已成为应对分布式计算中掉队者影响的关键框架。虽然多项式函数在现有编码计算方案下通常允许精确恢复，但非多项式函数需要从有限次评估中进行近似重构，这带来了重大挑战。因此，基于插值的非多项式编码计算方法受到关注，其中Berrut近似编码计算已成为最先进的方法。然而，由于Berrut插值基函数的全局支撑性，随着掉队者数量的增加，重构精度显著下降。为解决这一挑战，我们提出了一种基于三次B样条插值的编码计算框架。在我们的方法中，服务器端函数评估在主机处使用B样条进行重构，利用其局部支撑性和光滑性特性来增强稳定性和精度。我们提供了将B样条插值集成到编码计算中的系统方法，并对特定类光滑函数的近似误差推导了理论界。我们的分析表明，与基于Berrut的方法相比，本方法的误差界随工作者数量增加呈现更快的衰减速度。实验结果也证实，对于各类光滑非多项式函数，我们的方法相比基于Berrut的方法具有更高的精度。