Straggler-Aware Coded Polynomial Aggregation

Coded polynomial aggregation (CPA) in distributed computing systems enables the master to directly recover a weighted aggregation of polynomial computations without individually decoding each term, thereby reducing the number of required worker responses. However, existing CPA schemes are restricted to an idealized setting in which the system cannot tolerate stragglers. In this paper, we extend CPA to straggler-aware distributed computing systems with a pre-specified non-straggler pattern, where exact recovery is required for a given collection of admissible non-straggler sets. Our main results show that exact recovery of the desired aggregation is achievable with fewer worker responses than that required by polynomial codes based on individual decoding, and that feasibility is characterized by the intersection structure of the non-straggler patterns. In particular, we establish necessary and sufficient conditions for exact recovery in straggler-aware CPA. We identify an intersection-size threshold that is sufficient to guarantee exact recovery. When the number of admissible non-straggler sets is sufficiently large, we further show that this threshold is necessary in a generic sense. We also provide an explicit construction of feasible CPA schemes whenever the intersection size exceeds the derived threshold. Finally, simulations verify our theoretical results by demonstrating a sharp feasibility transition at the predicted intersection threshold.

💡 Research Summary

This paper extends the recently introduced Coded Polynomial Aggregation (CPA) framework to environments where some worker nodes may be stragglers, by exploiting a pre‑specified collection of admissible non‑straggler sets rather than requiring robustness against every possible straggler pattern. The authors consider a master‑worker system with N workers, K data matrices, a polynomial function F of degree d applied element‑wise, and a weight vector w that defines the desired weighted sum Y = Σₖ wₖ F(Xₖ). In the classic CPA setting the master encodes the data into an encoder polynomial E(z) evaluated at N distinct points βₙ, sends E(βₙ) to each worker, and each worker returns F(E(βₙ)). The master then interpolates a decoder polynomial D(z) from the received values and directly evaluates the weighted sum at the original data points αₖ, thereby avoiding the costly step of reconstructing each individual F(Xₖ).

The novelty of this work lies in relaxing the “all‑straggler‑sets” assumption. Instead of guaranteeing recovery for any subset of N−S responsive workers, the system is given a non‑straggler pattern 𝒩 = {𝒩_g}_{g=1}^G, where each 𝒩_g ⊂