Straggler-Aware Coded Polynomial Aggregation

2026-02-03

AI Summary

This work addresses the challenge posed by straggler nodes in distributed computing, which hinders the practical deployment of existing coded polynomial aggregation methods. We propose a straggler-aware coded aggregation framework that precisely characterizes the intersection structure among non-straggler node sets and establishes necessary and sufficient conditions for exact recovery of the weighted aggregation result. Theoretical analysis reveals that when the intersection size exceeds a specific threshold, the scheme is universally feasible in large-scale settings; this threshold not only ensures feasibility but also significantly reduces the number of required responsive nodes compared to conventional per-term decoding approaches. By integrating algebraic coding, polynomial interpolation, and combinatorial design, we construct an efficient coding scheme tailored to the intersection structure, and simulations confirm the predicted feasibility phase transition.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search
• Multiagent Systems: Mechanism Design

Application Category

• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

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.

Problem

• straggler tolerance
• coded polynomial aggregation
• distributed computing
• exact recovery
• non-straggler pattern

Innovation

• straggler-aware
• coded polynomial aggregation
• exact recovery
• intersection threshold
• distributed computing