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This paper presents fast first-order methods for solving linear programs (LPs) approximately. We adapt online linear programming algorithms to offline LPs and obtain algorithms that avoid any matrix multiplication. We also introduce a…
We observe that any $T(n)$ time algorithm (quantum or classical) for several central linear algebraic problems, such as computing $\det(A)$, $tr(A^3)$, or $tr(A^{-1})$ for an $n \times n$ integer matrix $A$, yields a $O(T(n)) + \tilde…
The quest for an algorithm that solves an $n\times n$ linear system in $O(n^2)$ time complexity, or $O(n^2 \text{poly}(1/\epsilon))$ when solving up to $\epsilon$ relative error, is a long-standing open problem in numerical linear algebra…
Autonomous systems embedded with machine learning modules often rely on deep neural networks for classifying different objects of interest in the environment or different actions or strategies to take for the system. Due to the…
Many scientific areas, from computer science to the environmental sciences and finance, give rise to multivariate time series which exhibit long memory, or loosely put, a slow decay in their autocorrelation structure. Efficient modelling…
Nonlinear time-history evolution problems employing high-fidelity physical models are essential in numerous scientific domains. However, these problems face a critical dual bottleneck: the immense computational cost of time-stepping and the…
In this paper, we study output feedback selection in linear time-invariant structured systems. We assume that the inputs and the outputs are dedicated, i.e., each input directly actuates a single state and each output directly senses a…
In this work, we develop the low-space Massively Parallel Computation (MPC) complexity landscape for a family of fundamental graph problems on trees. We present a general method that solves most locally checkable labeling (LCL) problems…
We survey some results on linear-time algorithms for systolic arrays. In particular, we show how the greatest common divisor (GCD) of two polynomials of degree n over a finite field can be computed in time O(n) on a linear systolic array of…
Given a linear system of equations $A\boldsymbol{x}=\boldsymbol{b}$, quantum linear system solvers (QLSSs) approximately prepare a quantum state $|\boldsymbol{x}\rangle$ for which the amplitudes are proportional to the solution vector…
We study tensor networks as a model of arithmetic computation for evaluating multilinear maps. These capture any algorithm based on low border rank tensor decompositions, such as $O(n^{\omega+\epsilon})$ time matrix multiplication, and in…
Computing has a huge memory problem. The memory system, consisting of multiple technologies at different levels, is responsible for most of the energy consumption, performance bottlenecks, robustness problems, monetary cost, and hardware…
Time series classification with missing data is a prevalent issue in time series analysis, as temporal data often contain missing values in practical applications. The traditional two-stage approach, which handles imputation and…
Large language models (LLMs) are increasingly deployed on complex reasoning tasks, yet little is known about their ability to internally evaluate problem difficulty, which is an essential capability for adaptive reasoning and efficient…
In recent years a large number of problems have been considered in external memory models of computation, where the complexity measure is the number of blocks of data that are moved between slow external memory and fast internal memory…
This paper studies the convergence rate of a continuous-time dynamical system for L1-minimization, known as the Locally Competitive Algorithm (LCA). Solving L1-minimization} problems efficiently and rapidly is of great interest to the…
Feedback optimization algorithms compute inputs to a system using real-time output measurements, which helps mitigate the effects of disturbances. However, existing work often models both system dynamics and computations in either discrete…
It is well known that many local graph problems, like Vertex Cover and Dominating Set, can be solved in 2^{O(tw)}|V|^{O(1)} time for graphs G=(V,E) with a given tree decomposition of width tw. However, for nonlocal problems, like the…
We prove that strong structural controllability of a pair of structural matrices $(\mathcal{A},\mathcal{B})$ can be verified in time linear in $n + r + \nu$, where $\mathcal{A}$ is square, $n$ and $r$ denote the number of columns of…
We construct fast algorithms for evaluating transforms associated with families of functions which satisfy recurrence relations. These include algorithms both for computing the coefficients in linear combinations of the functions, given the…