Distributed Matrix-Vector Multiplication with Sparsity and Privacy Guarantees

Xhemrishi, Marvin; Bitar, Rawad; Wachter-Zeh, Antonia

doi:10.1109/isit50566.2022.9834805

Cited by 9 publications

(2 citation statements)

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“…There are a number of directions for the future work of this paper. While there are several secure distributed matrix computation schemes [15]- [18] which protect the system against privacy leakage, most of them add dense random matrices to the coded submatrices which destroy the sparsity of the assigned submatrices. Thus, a straggler resilient secure coded scheme needs to be developed which is particularly suitable for sparse input matrices.…”

Section: Discussionmentioning

confidence: 99%

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Distributed Matrix Computations with Low-weight Encodings

Das¹,

Ramamoorthy²,

Love³

et al. 2023

Preprint

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Straggler nodes are well-known bottlenecks of distributed matrix computations which induce reductions in computation/communication speeds. A common strategy for mitigating such stragglers is to incorporate Reed-Solomon based MDS (maximum distance separable) codes into the framework; this can achieve resilience against an optimal number of stragglers. However, these codes assign dense linear combinations of submatrices to the worker nodes. When the input matrices are sparse, these approaches increase the number of non-zero entries in the encoded matrices, which in turn adversely affects the worker computation time. In this work, we develop a distributed matrix computation approach where the assigned encoded submatrices are random linear combinations of a small number of submatrices.In addition to being well suited for sparse input matrices, our approach continues have the optimal straggler resilience in a certain range of problem parameters. Moreover, compared to recent sparse matrix computation approaches, the search for a "good" set of random coefficients to promote numerical stability in our method is much more computationally efficient. We show that our approach can efficiently utilize partial computations done by slower worker nodes in a heterogeneous system which can enhance the overall computation speed. Numerical experiments conducted through Amazon Web Services (AWS) demonstrate up to 30% reduction in per worker node computation time and 100× faster encoding compared to the available methods.

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Section: Discussionmentioning

confidence: 99%

“…Several coded computation schemes have been proposed for matrix multiplication [1]- [9], [12], [13], [15]- [20] in recent years. We give a comparative summary between these schemes in terms of properties they support in Table I; for a more detailed overview, we refer the reader to [11].…”

Section: B Background and Literature Reviewmentioning

confidence: 99%