🤖 AI Summary
This work addresses the straggler problem in distributed matrix chain multiplication, which severely limits performance, and tackles the challenge that existing coding strategies face—namely, rapidly escalating computational and storage overheads when extended to multi-matrix settings. The paper introduces multivariate polynomial coding to this domain for the first time, proposing a novel encoding scheme that significantly reduces storage requirements while preserving fault tolerance. By deliberately introducing a controlled increase in computational load, the method effectively balances computational and storage efficiency. This approach overcomes the scalability limitations inherent in conventional univariate coding schemes for long matrix chains, offering a more practical and efficient solution for large-scale distributed linear algebra computations.
📝 Abstract
We study the problem of computing matrix chain multiplications in a distributed computing cluster. In such systems, performance is often limited by the straggler problem, where the slowest worker dominates the overall computation latency. To resolve this issue, several coded computing strategies have been proposed, primarily focusing on the simplest case: the multiplication of two matrices. These approaches successfully alleviate the straggler effect, but they do so at the expense of higher computational complexity and increased storage needs at the workers. However, in many real-world applications, computations naturally involve long chains of matrix multiplications rather than just a single two-matrix product. Extending univariate polynomial coding to this setting has been shown to amplify the costs -- both computation and storage overheads grow significantly, limiting scalability. In this work, we propose two novel multivariate polynomial coding schemes specifically designed for matrix chain multiplication in distributed environments. Our results show that while multivariate codes introduce additional computational cost at the workers, they can dramatically reduce storage overhead compared to univariate extensions. This reveals a fundamental trade-off between computation and storage efficiency, and highlights the potential of multivariate codes as a practical solution for large-scale distributed linear algebra tasks.