Coded sparse matrix computation schemes that leverage partial stragglers

Das, Anindya Bijoy; Ramamoorthy, Aditya

doi:10.1109/isit45174.2021.9518059

Cited by 13 publications

(36 citation statements)

References 10 publications

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“…In this section we combine our coding strategy with the cyclically shifted task assignment from [14] and [33] to obtain our coded computing scheme that is resilient to stragglers. The reason for choosing this assignment scheme is that it perfectly preserves the sparsity of the input tasks, R and A + R.…”

Section: Coded Computing With Sparsity and Privacy Guaranteesmentioning

confidence: 99%

“…Each worker starts by computing the task of layer 1 and proceeds to the next layer after completing this task. We use the same proof technique as in [14]. Without loss of generality we will analyse the minimum number of responses needed from the partly trusted cluster.…”

Section: Proof Privacymentioning

confidence: 99%

“…Destroying the sparsity of the input matrices may incur artificial delays at the computing nodes. Hence, coding-theoretic techniques maintaining the sparsity of the underlying matrices and mitigating the stragglers are investigated [13], [14].…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, the works in [17]- [19], [24]- [27] consider double-sided privacy, i.e., the setting of matrix-matrix multiplication in which both input matrices must be kept private. The works of [13] and [14] are among the first that consider a sparsity-preserving coded computing scenario. In [13], the authors consider a matrix-matrix multiplication where both input matrices are sparse.…”

Section: Introductionmentioning

confidence: 99%

“…The matrices are encoded using Fountain codes [28] with a custom-made degree distribution to ensure sparsity. The authors of [14] consider, among other scenarios, a distributed matrix-vector multiplication setting in which the input data is partitioned into smaller matrices. Those matrices are then distributed to the processing units using a fractional repetition code to mitigate stragglers.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Distributed Matrix-Vector Multiplication with Sparsity and Privacy Guarantees

Xhemrishi¹,

Bitar²,

Wachter-Zeh³

2022

Preprint

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We consider the problem of designing a coding scheme that allows both sparsity and privacy for distributed matrix-vector multiplication. Perfect information-theoretic privacy requires encoding the input sparse matrices into matrices distributed uniformly at random from the considered alphabet; thus destroying the sparsity. Computing matrix-vector multiplication for sparse matrices is known to be fast. Distributing the computation over the non-sparse encoded matrices maintains privacy, but introduces artificial computing delays. In this work, we relax the privacy constraint and show that a certain level of sparsity can be maintained in the encoded matrices. We consider the chief/worker setting while assuming the presence of two clusters of workers: one is completely untrusted in which all workers collude to eavesdrop on the input matrix and in which perfect privacy must be satisfied; in the partly trusted cluster, only up to z workers may collude and to which revealing small amount of information about the input matrix is allowed. We design a scheme that trades sparsity for privacy while achieving the desired constraints. We use cyclic task assignments of the encoded matrices to tolerate partial and full stragglers.

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Section: Coded Computing With Sparsity and Privacy Guaranteesmentioning

confidence: 99%

Section: Proof Privacymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%