Related papers: Fast ultrametric matrix-vector multiplication
The Strassen algorithm and Winograd's variant accelerate matrix multiplication by using fewer arithmetic operations than standard matrix multiplication. Although many papers have been published to accelerate single- as well as…
Accelerators for sparse matrix multiplication are important components in emerging systems. In this paper, we study the main challenges of accelerating Sparse Matrix Multiplication (SpMM). For the situations that data is not stored in the…
In this work the algorithms of fast multiplication of matrices are considered. To any algorithm there associated a certain group of automorphisms. These automorphism groups are found for some well-known algorithms, including algorithms of…
The purpose of this text is to provide an accessible introduction to a set of recently developed algorithms for factorizing matrices. These new algorithms attain high practical speed by reducing the dimensionality of intermediate…
Generalized sparse matrix-matrix multiplication is a key primitive for many high performance graph algorithms as well as some linear solvers such as multigrid. We present the first parallel algorithms that achieve increasing speedups for an…
Net-trees are a general purpose data structure for metric data that have been used to solve a wide range of algorithmic problems. We give a simple randomized algorithm to construct net-trees on doubling metrics using $O(n\log n)$ time in…
In this paper, we propose the distributed tree kernels (DTK) as a novel method to reduce time and space complexity of tree kernels. Using a linear complexity algorithm to compute vectors for trees, we embed feature spaces of tree fragments…
We combine the known methods for univariate polynomial root-finding and for computations in the Frobenius matrix algebra with our novel techniques to advance numerical solution of a univariate polynomial equation, and in particular…
Quaternion symmetry is ubiquitous in the physical sciences. As such, much work has been afforded over the years to the development of efficient schemes to exploit this symmetry using real and complex linear algebra. Recent years have also…
We present linear-time algorithms for partitioning a path or a tree with weights on the vertices by removing $k$ edges to maximize the minimum-weight component. We also use the same framework to partition a path with weight on the vertices,…
We present a new paradigm for speeding up randomized computations of several frequently used functions in machine learning. In particular, our paradigm can be applied for improving computations of kernels based on random embeddings. Above…
Cohn and Umans proposed a framework for developing fast matrix multiplication algorithms based on the embedding computation in certain groups algebras. In subsequent work with Kleinberg and Szegedy, they connected this to the search for…
The problem of realizing finite metric spaces in terms of weighted graphs has many applications. For example, the mathematical and computational properties of metrics that can be realized by trees have been well-studied and such research…
Efficient discovery of frequent itemsets in large datasets is a crucial task of data mining. In recent years, several approaches have been proposed for generating high utility patterns, they arise the problems of producing a large number of…
Matrix multiplication is a fundamental building block for large scale computations arising in various applications, including machine learning. There has been significant recent interest in using coding to speed up distributed matrix…
We present quadrature schemes to calculate matrices, where the so-called modified Hilbert transformation is involved. These matrices occur as temporal parts of Galerkin finite element discretizations of parabolic or hyperbolic problems when…
We present a polynomial time dynamic programming algorithm for optimal partitions in the shortest path metric induced by a tree. This resolves, among other things, the exact complexity status of the optimal partition problems in one…
An efficient algorithm for computing eigenvectors of a matrix of integers by exact computation is proposed. The components of calculated eigenvectors are expressed as polynomials in the eigenvalue to which the eigenvector is associated, as…
We consider the problem of embedding a subset of $\mathbb{R}^n$ into a low-dimensional Hamming cube in an almost isometric way. We construct a simple, data-oblivious, and computationally efficient map that achieves this task with high…
In this paper, we introduce novel fast matrix inversion algorithms that leverage triangular decomposition and recurrent formalism, incorporating Strassen's fast matrix multiplication. Our research places particular emphasis on triangular…