Distributed Matrix-Vector Multiplication with Sparsity and Privacy Guarantees

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.

Multi-User Linearly-Separable Distributed Computing

“…As the complexity of these tasks increases, research seeks novel parallel processing techniques to efficiently offload computations to groups of distributed servers, under various frameworks such as MapReduce [1] and Spark [2]. Distributed computing naturally entails several challenges that involve accuracy [3]- [5], scalability [6]- [10], privacy and security [11]- [23], as well as latency and straggler mitigation [24]- [31]. For a detailed survey of related research works, the reader is referred to [32], [33].…”