Related papers: Spectral sparsification of matrix inputs as a prep…
Spectral graph sparsification is a classical tool for reducing graph complexity while preserving Laplacian quadratic forms. In graph neural networks (GNNs), sparsification is often used to accelerate computation while maintaining predictive…
We present a nearly-linear time algorithm that produces high-quality sparsifiers of weighted graphs. Given as input a weighted graph $G=(V,E,w)$ and a parameter $\epsilon>0$, we produce a weighted subgraph $H=(V,\tilde{E},\tilde{w})$ of $G$…
Matrix powering is a fundamental computational primitive in linear algebra. It has widespread applications in scientific computing and engineering, and underlies the solution of time-homogeneous linear ordinary differential equations,…
In this paper, we generalize Spencer's hyperbolic cosine algorithm to the matrix-valued setting. We apply the proposed algorithm to several problems by analyzing its computational efficiency under two special cases of matrices; one in which…
We propose new quantum algorithms for estimating spectral sums of positive semi-definite (PSD) matrices. The spectral sum of an PSD matrix $A$, for a function $f$, is defined as $ \text{Tr}[f(A)] = \sum_j f(\lambda_j)$, where $\lambda_j$…
In recent years, spectral graph sparsification techniques that can compute ultra-sparse graph proxies have been extensively studied for accelerating various numerical and graph-related applications. Prior nearly-linear-time spectral…
Recent spectral graph sparsification techniques have shown promising performance in accelerating many numerical and graph algorithms, such as iterative methods for solving large sparse matrices, spectral partitioning of undirected graphs,…
Stochastic scientific models and machine learning optimization estimators have a large number of variables; hence computing large sparse Jacobians and Hessians is important. Algorithmic differentiation (AD) greatly reduces the programming…
We introduce a new approach to spectral sparsification that approximates the quadratic form of the pseudoinverse of a graph Laplacian restricted to a subspace. We show that sparsifiers with a near-linear number of edges in the dimension of…
This paper introduces the sparsifying preconditioner for the pseudospectral approximation of highly indefinite systems on periodic structures, which include the frequency-domain response problems of the Helmholtz equation and the…
Spectral sparsification is a general technique developed by Spielman et al. to reduce the number of edges in a graph while retaining its structural properties. We investigate the use of spectral sparsification to produce good visual…
One of the core research questions in the theory of quantum computing is to find out to what precise extent the classical simulation of a noisy quantum circuits is possible and where potential quantum advantages can set in. In this work, we…
Graphs naturally appear in several real-world contexts including social networks, the web network, and telecommunication networks. While the analysis and the understanding of graph structures have been a central area of study in algorithm…
A graph G'(V,E') is an \eps-sparsification of G for some \eps>0, if every (weighted) cut in G' is within (1\pm \eps) of the corresponding cut in G. A celebrated result of Benczur and Karger shows that for every undirected graph G, an…
Spectral clustering is a fundamental method for graph partitioning, but its reliance on eigenvector computation limits scalability to massive graphs. Classical sparsification methods preserve spectral properties by sampling edges…
We introduce a novel hybrid quantum-analog algorithm to perform graph clustering that exploits connections between the evolution of dynamical systems on graphs and the underlying graph spectra. This approach constitutes a new class of…
Various algorithms have been developed to simulate quantum circuits on classical hardware. Among the most prominent are approaches based on \emph{stabilizer decompositions} and \emph{tensor network contraction}. In this work, we present a…
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…
Quantum walks provide a natural framework to approach graph problems with quantum computers, exhibiting speedups over their classical counterparts for tasks such as the search for marked nodes or the prediction of missing links.…
Recently, there has been a surge of interest for quantum computation for its ability to exponentially speed up algorithms, including machine learning algorithms. However, Tang suggested that the exponential speed up can also be done on a…