Related papers: Matrix Multiplication in the MPC Model
We study two fundamental optimization problems: (1) scaling a symmetric positive definite matrix by a positive diagonal matrix so that the resulting matrix has row and column sums equal to 1; and (2) minimizing a quadratic function subject…
A generalization of recent group-theoretic matrix multiplication algorithms to an analogue of the theory of partial matrix multiplication is presented. We demonstrate that the added flexibility of this approach can in some cases improve…
An alternative to the matrix inverse procedure is presented. Given a bit register which is arbitrarily large, the matrix inverse to an arbitrarily large matrix can be peformed in ${\cal O}(N^2)$ operations, and to matrix multiplication on a…
Hierarchical matrices approximate a given matrix by a decomposition into low-rank submatrices that can be handled efficiently in factorized form. $\mathcal{H}^2$-matrices refine this representation following the ideas of fast multipole…
In this paper, we study the $d$-dimensional update-query problem. We provide lower bounds on update and query running times, assuming a long-standing conjecture on min-plus matrix multiplication, as well as algorithms that are close to the…
Ootomo, Ozaki, and Yokota [Int. J. High Perform. Comput. Appl., 38 (2024), p. 297-313] have proposed a strategy to recast a floating-point matrix multiplication in terms of integer matrix products. The factors A and B are split into integer…
We provide novel coded computation strategies for distributed matrix-matrix products that outperform the recent "Polynomial code" constructions in recovery threshold, i.e., the required number of successful workers. When $m$-th fraction of…
Vector-Matrix Multiplication (VMM) is the fundamental and frequently required computation in inference of Neural Networks (NN). Due to the large data movement required during inference, VMM can benefit greatly from in-memory computing.…
Distributed matrix multiplication is widely used in several scientific domains. It is well recognized that computation times on distributed clusters are often dominated by the slowest workers (called stragglers). Recent work has…
We present a method for parallel block-sparse matrix-matrix multiplication on distributed memory clusters. By using a quadtree matrix representation, data locality is exploited without prior information about the matrix sparsity pattern. A…
Matrix-matrix multiplication is a basic operation in linear algebra and an essential building block for a wide range of algorithms in various scientific fields. Theory and implementation for the dense, square matrix case are well-developed.…
We study the minimum spanning tree (MST) problem in the massively parallel computation (MPC) model. Our focus is particularly on the *strictly sublinear* regime of MPC where the space per machine is $O(n^\delta)$. Here $n$ is the number of…
We consider the classic $k$-center problem {in the constant dimensional Euclidean space} under a parallel setting, on the low-local-space Massively Parallel Computation (MPC) model, with local space per machine of ${O}(n^{\delta})$, where…
Secure Multi-party Computation (MPC) enables untrusted parties to jointly compute a function without revealing their inputs. Its application to machine learning (ML) has gained significant attention, particularly for secure inference…
We present a non-commutative algorithm for multiplying (7x7) matrices using 250 multiplications and a non-commutative algorithm for multiplying (9x9) matrices using 520 multiplications. These algorithms are obtained using the same…
Until a few years ago, the fastest known matrix multiplication algorithm, due to Coppersmith and Winograd (1990), ran in time $O(n^{2.3755})$. Recently, a surge of activity by Stothers, Vassilevska-Williams, and Le Gall has led to an…
Solving dual quaternion equations is an important issue in many fields such as scientific computing and engineering applications. In this paper, we first introduce a new metric function for dual quaternion matrices. Then, we reformulate…
We investigate the problem of factorizing a matrix into several sparse matrices and propose an algorithm for this under randomness and sparsity assumptions. This problem can be viewed as a simplification of the deep learning problem where…
Karppa & Kaski (2019) proposed a novel ``broken" or ``opportunistic" matrix multiplication algorithm, based on a variant of Strassen's algorithm, and used this to develop new algorithms for Boolean matrix multiplication, among other tasks.…
In this paper, we consider the following inverse maintenance problem: given $A \in \mathbb{R}^{n\times d}$ and a number of rounds $r$, we receive a $n\times n$ diagonal matrix $D^{(k)}$ at round $k$ and we wish to maintain an efficient…