Basis-Spline Assisted Coded Computing: Strategies and Error Bounds

TL;DR

This paper introduces a novel coded computing framework using cubic B-spline interpolation to improve the accuracy and stability of reconstructing smooth non-polynomial functions in distributed systems, addressing limitations of existing methods.

Contribution

It proposes a B-spline based interpolation method for coded computing, providing theoretical error bounds and demonstrating improved accuracy over Berrut-based approaches.

Findings

Error bounds decay faster with more workers

B-spline approach outperforms Berrut in accuracy

Method effectively reconstructs smooth non-polynomial functions

Abstract

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.