Coded computing has become a key framework for reliable distributed computation over decentralized networks, effectively mitigating the impact of stragglers. Although there exists a wide range of coded computing methods to handle both polynomial and non-polynomial functions, computing methods for the latter class have received traction due its inherent challenges in reconstructing non-polynomial functions using a finite number of evaluations. Among them, the state-of-the-art method is Berrut Approximated coded computing, wherein Berrut interpolants, are used for approximating the non-polynomial function. However, since Berrut interpolants have global support characteristics, such methods are known to offer degraded accuracy when the number of stragglers is large. 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 node 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 in terms of the number of servers and stragglers. Comparative analysis demonstrates that our framework significantly outperforms Berrut-based methods for various non-polynomial functions.

翻译：编码计算已成为去中心化网络中可靠分布式计算的关键框架，能有效缓解掉队节点的影响。尽管已有多种编码计算方法用于处理多项式与非多项式函数，但由于利用有限次函数值重构非多项式函数存在固有挑战，针对后者的计算方法备受关注。其中，最先进的方法是Berrut近似编码计算，该方法采用Berrut插值函数来近似非多项式函数。然而，由于Berrut插值函数具有全局支撑特性，当掉队节点数量较多时，此类方法的精度会显著下降。为解决这一难题，我们提出了一种基于三次B样条插值的编码计算框架。在该方法中，主节点利用B样条的局部支撑性和光滑特性重构服务器端的函数求值，从而提升计算稳定性与精度。我们提出了将B样条插值系统化集成到编码计算中的方法论，并推导了关于服务器数量与掉队节点数量的近似误差理论界。对比分析表明，对于各类非多项式函数，本框架性能显著优于基于Berrut的方法。