Distributed Matrix-Vector Multiplication with Sparsity and Privacy Guarantees

TL;DR

This paper introduces a novel distributed matrix-vector multiplication scheme that balances sparsity and privacy constraints, allowing for efficient computation with controlled privacy leakage in multi-cluster settings.

Contribution

It proposes a new coding scheme that relaxes privacy requirements to preserve sparsity and efficiency in distributed computations with multiple worker clusters.

Findings

Achieves a trade-off between sparsity and privacy in distributed matrix-vector multiplication.

Supports cyclic task assignments to tolerate stragglers.

Handles different trust levels among worker clusters.

Abstract

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.