Related papers: Sparse Matrix Multiplication in the Low-Bandwidth …
Matrix computations are a fundamental building-block of edge computing systems, with a major recent uptick in demand due to their use in AI/ML training and inference procedures. Existing approaches for distributing matrix computations…
Randomized sampling has recently been demonstrated to be an efficient technique for computing approximate low-rank factorizations of matrices for which fast methods for computing matrix vector products are available. This paper describes an…
This paper aims to propose and theoretically analyze a new distributed scheme for sparse linear regression and feature selection. The primary goal is to learn the few causal features of a high-dimensional dataset based on noisy observations…
This paper presents an adaptive randomized algorithm for computing the butterfly factorization of a $m\times n$ matrix with $m\approx n$ provided that both the matrix and its transpose can be rapidly applied to arbitrary vectors. The…
We address the problems of minimizing and of maximizing the spectral radius overa compact family of non-negative matrices. Those problems being hard in generalcan be efficiently solved for some special families. We consider the so-called…
Computationally efficient matrix multiplication is a fundamental requirement in various fields, including and particularly in data analytics. To do so, the computation task of a large-scale matrix multiplication is typically outsourced to…
The conjectured hardness of Boolean matrix-vector multiplication has been used with great success to prove conditional lower bounds for numerous important data structure problems, see Henzinger et al. [STOC'15]. In recent work, Larsen and…
Herein we explore a dual tree algorithm for matrix multiplication of $A\in \mathbb{R}^{M\times D}$ and $B\in\mathbb{R}^{D\times N}$, very narrowly effective if the normalized rows of $A$ and columns of $B$, treated as vectors in…
In distributed matrix multiplication, a common scenario is to assign each worker a fraction of the multiplication task, by partitioning the input matrices into smaller submatrices. In particular, by dividing two input matrices into…
It is widely known that the lower bound for the algorithmic complexity of square matrix multiplication resorts to at least $n^2$ arithmetic operations. The justification builds upon the following reasoning: given that there are $2 n^2$…
The communication cost of algorithms (also known as I/O-complexity) is shown to be closely related to the expansion properties of the corresponding computation graphs. We demonstrate this on Strassen's and other fast matrix multiplication…
For a matrix $A\in \mathbb{R}^{n\times d}$ with $n\geq d$, we consider the dual problems of $\min \|Ax-b\|_p^p, \, b\in \mathbb{R}^n$ and $\min_{A^\top x=b} \|x\|_p^p,\, b\in \mathbb{R}^d$. We improve the runtimes for solving these problems…
Finding a small spectral approximation for a tall $n \times d$ matrix $A$ is a fundamental numerical primitive. For a number of reasons, one often seeks an approximation whose rows are sampled from those of $A$. Row sampling improves…
The success of modern parallel paradigms such as MapReduce, Hadoop, or Spark, has attracted a significant attention to the Massively Parallel Computation (MPC) model over the past few years, especially on graph problems. In this work, we…
In the Sparse Linear Regression (SLR) problem, given a $d \times n$ matrix $M$ and a $d$-dimensional query $q$, the goal is to compute a $k$-sparse $n$-dimensional vector $\tau$ such that the error $||M \tau-q||$ is minimized. This problem…
In this paper we study the two player randomized communication complexity of the sparse set disjointness and the exists-equal problems and give matching lower and upper bounds (up to constant factors) for any number of rounds for both of…
Matrix recovery from sparse observations is an extensively studied topic emerging in various applications, such as recommendation system and signal processing, which includes the matrix completion and compressed sensing models as special…
We give an efficient algorithm for finding sparse approximate solutions to linear systems of equations with nonnegative coefficients. Unlike most known results for sparse recovery, we do not require {\em any} assumption on the matrix other…
Miller et al. \cite{MPVX15} devised a distributed\footnote{They actually showed a PRAM algorithm. The distributed algorithm with these properties is implicit in \cite{MPVX15}.} algorithm in the CONGEST model, that given a parameter $k =…
Kernel matrices appear in machine learning and non-parametric statistics. Given $N$ points in $d$ dimensions and a kernel function that requires $\mathcal{O}(d)$ work to evaluate, we present an $\mathcal{O}(dN\log N)$-work algorithm for the…