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Straggler Mitigation in Distributed Matrix Multiplication: Fundamental Limits and Optimal Coding | IEEE Journals & Magazine | IEEE Xplore

Straggler Mitigation in Distributed Matrix Multiplication: Fundamental Limits and Optimal Coding


Abstract:

We consider the problem of massive matrix multiplication, which underlies many data analytic applications, in a large-scale distributed system comprising a group of worke...Show More

Abstract:

We consider the problem of massive matrix multiplication, which underlies many data analytic applications, in a large-scale distributed system comprising a group of worker nodes. We target the stragglers' delay performance bottleneck, which is due to the unpredictable latency in waiting for slowest nodes (or stragglers) to finish their tasks. We propose a novel coding strategy, named entangled polynomial code, for designing the intermediate computations at the worker nodes in order to minimize the recovery threshold (i.e., the number of workers that we need to wait for in order to compute the final output). We demonstrate the optimality of entangled polynomial code in several cases, and show that it provides orderwise improvement over the conventional schemes for straggler mitigation. Furthermore, we characterize the optimal recovery threshold among all linear coding strategies within a factor of 2 using bilinear complexity, by developing an improved version of the entangled polynomial code. In particular, while evaluating bilinear complexity is a well-known challenging problem, we show that optimal recovery threshold for linear coding strategies can be approximated within a factor of 2 of this fundamental quantity. On the other hand, the improved version of the entangled polynomial code enables further and orderwise reduction in the recovery threshold, compared to its basic version. Finally, we show that the techniques developed in this paper can also be extended to several other problems such as coded convolution and fault-tolerant computing, leading to tight characterizations.
Published in: IEEE Transactions on Information Theory ( Volume: 66, Issue: 3, March 2020)
Page(s): 1920 - 1933
Date of Publication: 03 January 2020

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