Related papers: The Input/Output Complexity of Sparse Matrix Multi…
We study matrix multiplication in the low-bandwidth model: There are $n$ computers, and we need to compute the product of two $n \times n$ matrices. Initially computer $i$ knows row $i$ of each input matrix. In one communication round each…
What is the time complexity of matrix multiplication of sparse integer matrices with $m_{in}$ nonzeros in the input and $m_{out}$ nonzeros in the output? This paper provides improved upper bounds for this question for almost any choice of…
A tight lower bound for required I/O when computing an ordinary matrix-matrix multiplication on a processor with two layers of memory is established. Prior work obtained weaker lower bounds by reasoning about the number of segments needed…
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…
In 1981 Hong and Kung proved a lower bound on the amount of communication needed to perform dense, matrix-multiplication using the conventional $O(n^3)$ algorithm, where the input matrices were too large to fit in the small, fast memory. In…
Asymptotically tight lower bounds are derived for the I/O complexity of a general class of hybrid algorithms computing the product of $n \times n$ square matrices combining ``\emph{Strassen-like}'' fast matrix multiplication approach with…
Multiplication of a sparse matrix with another (dense or sparse) matrix is a fundamental operation that captures the computational patterns of many data science applications, including but not limited to graph algorithms, sparsely connected…
Many real-world data sets are sparse or almost sparse. One method to measure this for a matrix $A\in \mathbb{R}^{n\times n}$ is the \emph{numerical sparsity}, denoted $\mathsf{ns}(A)$, defined as the minimum $k\geq 1$ such that…
We give two algorithms for output-sparse matrix multiplication (OSMM), the problem of multiplying two $n \times n$ matrices $A, B$ when their product $AB$ is promised to have at most $O(n^{\delta})$ many non-zero entries for a given value…
Linear-scaling electronic-structure techniques, also called O(N) techniques, rely heavily on the multiplication of sparse matrices, where the sparsity arises from spatial cut-offs. In order to treat very large systems, the calculations must…
Sparse matrix multiplication is an important component of linear algebra computations. Implementing sparse matrix multiplication on an associative processor (AP) enables high level of parallelism, where a row of one matrix is multiplied in…
To preserve data privacy, multi-party computation (MPC) enables executing Machine Learning (ML) algorithms on private data. However, MPC frameworks do not include optimized operations on sparse data. This absence makes them unsuitable for…
We present an algorithm to reduce the computational effort for the multiplication of a given matrix with an unknown column vector. The algorithm decomposes the given matrix into a product of matrices whose entries are either zero or integer…
Approximate matrix multiplication with limited space has received ever-increasing attention due to the emergence of large-scale applications. Recently, based on a popular matrix sketching algorithm -- frequent directions, previous work has…
We consider the problem of doing fast and reliable estimation of the number of non-zero entries in a sparse boolean matrix product. This problem has applications in databases and computer algebra. Let n denote the total number of non-zero…
This paper studies a high-dimensional inference problem involving the matrix tensor product of random matrices. This problem generalizes a number of contemporary data science problems including the spiked matrix models used in sparse…
In a large-scale and distributed matrix multiplication problem $C=A^{\intercal}B$, where $C\in\mathbb{R}^{r\times t}$, the coded computation plays an important role to effectively deal with "stragglers" (distributed computations that may…
We study the problem of constructing explicit families of matrices which cannot be expressed as a product of a few sparse matrices. In addition to being a natural mathematical question on its own, this problem appears in various…
Min-plus matrix multiplication is used in many problems operating on distances in graphs or solvable by dynamic programming. Assuming the APSP hypothesis, there is no subcubic-time algorithm for the min-plus product of two general $n\times…
We consider the problem of sparse matrix multiplication by the column row method in a distributed setting where the matrix product is not necessarily sparse. We present a surprisingly simple method for "consistent" parallel processing of…