Related papers: Erasure coding for distributed matrix multiplicati…
Owing to data-intensive large-scale applications, distributed computation systems have gained significant recent interest, due to their ability of running such tasks over a large number of commodity nodes in a time efficient manner. One of…
An $(m,n,a,b)$-tensor code consists of $m\times n$ matrices whose columns satisfy `$a$' parity checks and rows satisfy `$b$' parity checks (i.e., a tensor code is the tensor product of a column code and row code). Tensor codes are useful in…
We exploit the truncated singular value decomposition and the recently proposed circulant decomposition for an efficient first-order approximation of the multiplication of large dense matrices. A decomposition of each matrix into a sum of a…
The performance of large-scale distributed compute systems is adversely impacted by stragglers when the execution time of a job is uncertain. To manage stragglers, we consider a multi-fork approach for job scheduling, where additional…
This work investigates the design of sparse secret sharing schemes that encode a sparse private matrix into sparse shares. This investigation is motivated by distributed computing, where the multiplication of sparse and private matrices is…
In modern computer systems, jobs are divided into short tasks and executed in parallel. Empirical observations in practical systems suggest that the task service times are highly random and the job service time is bottlenecked by the…
Reducing communication - either between levels of a memory hierarchy or between processors over a network - is a key component of performance optimization (in both time and energy) for many problems, including dense linear algebra, particle…
This paper considers the problem of matrix completion when some number of the columns are completely and arbitrarily corrupted, potentially by a malicious adversary. It is well-known that standard algorithms for matrix completion can return…
In many statistical linear inverse problems, one needs to recover classes of similar curves from their noisy images under an operator that does not have a bounded inverse. Problems of this kind appear in many areas of application.…
Erasure codes are being increasingly used in distributed-storage systems in place of data-replication, since they provide the same level of reliability with much lower storage overhead. We consider the problem of constructing explicit…
In prior work, Gupta et al. (SPAA 2022) presented a distributed algorithm for multiplying sparse $n \times n$ matrices, using $n$ computers. They assumed that the input matrices are uniformly sparse--there are at most $d$ non-zeros in each…
Distributed linearly separable computation, where a user asks some distributed servers to compute a linearly separable function, was recently formulated by the same authors and aims to alleviate the bottlenecks of stragglers and…
In this work, a graph partitioning problem in a fixed number of connected components is considered. Given an undirected graph with costs on the edges, the problem consists of partitioning the set of nodes into a fixed number of subsets with…
Coded computing has emerged as a promising framework for tackling significant challenges in large-scale distributed computing, including the presence of slow, faulty, or compromised servers. In this approach, each worker node processes a…
Gradient descent and its many variants, including mini-batch stochastic gradient descent, form the algorithmic foundation of modern large-scale machine learning. Due to the size and scale of modern data, gradient computations are often…
A major hurdle in machine learning is scalability to massive datasets. One approach to overcoming this is to distribute the computational tasks among several workers. \textit{Gradient coding} has been recently proposed in distributed…
We consider the problem of designing rateless coded private distributed matrix-matrix multiplication. A master server owns two private matrices $\mathbf{A}$ and $\mathbf{B}$ and wants to hire worker nodes to help compute the multiplication.…
We propose splitting methods for the computation of the exponential of perturbed matrices which can be written as the sum $A=D+\varepsilon B$ of a sparse and efficiently exponentiable matrix $D$ with sparse exponential $e^D$ and a dense…
We introduce a new approach to proving that a sequence of deterministic linear codes achieves capacity on an erasure channel under maximum a posteriori decoding. Rather than relying on the precise structure of the codes our method exploits…
In standard clustering problems, data points are represented by vectors, and by stacking them together, one forms a data matrix with row or column cluster structure. In this paper, we consider a class of binary matrices, arising in many…