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We give a faster algorithm for computing an approximate John ellipsoid around $n$ points in $d$ dimensions. The best known prior algorithms are based on repeatedly computing the leverage scores of the points and reweighting them by these…

Data Structures and Algorithms · Computer Science 2025-01-06 David P. Woodruff , Taisuke Yasuda

This paper describes a new algorithm for computing a low-Tucker-rank approximation of a tensor. The method applies a randomized linear map to the tensor to obtain a sketch that captures the important directions within each mode, as well as…

Numerical Analysis · Mathematics 2021-05-04 Yiming Sun , Yang Guo , Charlene Luo , Joel Tropp , Madeleine Udell

Detecting elliptical objects from an image is a central task in robot navigation and industrial diagnosis where the detection time is always a critical issue. Existing methods are hardly applicable to these real-time scenarios of limited…

Computer Vision and Pattern Recognition · Computer Science 2017-08-02 Qi Jia , Xin Fan , Zhongxuan Luo , Lianbo Song , Tie Qiu

In this paper, we show that if the optimization function is restricted-strongly-convex (RSC) and restricted-smooth (RSM) -- a rich subclass of weakly submodular functions -- then a streaming algorithm with constant factor approximation…

Machine Learning · Computer Science 2018-07-24 Karthik S. Gurumoorthy , Amit Dhurandhar

We propose a new method for unconstrained optimization of a smooth and strongly convex function, which attains the optimal rate of convergence of Nesterov's accelerated gradient descent. The new algorithm has a simple geometric…

Optimization and Control · Mathematics 2015-06-30 Sébastien Bubeck , Yin Tat Lee , Mohit Singh

We present a simple deterministic single-pass $(2+\epsilon)$-approximation algorithm for the maximum weight matching problem in the semi-streaming model. This improves upon the currently best known approximation ratio of $(4+\epsilon)$. Our…

Data Structures and Algorithms · Computer Science 2018-11-07 Ami Paz , Gregory Schwartzman

This paper argues that randomized linear sketching is a natural tool for on-the-fly compression of data matrices that arise from large-scale scientific simulations and data collection. The technical contribution consists in a new algorithm…

Numerical Analysis · Computer Science 2019-02-26 Joel A. Tropp , Alp Yurtsever , Madeleine Udell , Volkan Cevher

Non-linear Trajectory Optimisation (TO) methods require good initial guesses to converge to a locally optimal solution. A feasible guess can often be obtained by allocating a large amount of time for the trajectory to complete. However for…

Robotics · Computer Science 2022-03-16 Steve Tonneau

Work on approximate linear algebra has led to efficient distributed and streaming algorithms for problems such as approximate matrix multiplication, low rank approximation, and regression, primarily for the Euclidean norm $\ell_2$. We study…

Data Structures and Algorithms · Computer Science 2018-07-10 Graham Cormode , Charlie Dickens , David P. Woodruff

We initiate a broad study of classical problems in the streaming model with insertions and deletions in the setting where we allow the approximation factor $\alpha$ to be much larger than $1$. Such algorithms can use significantly less…

Data Structures and Algorithms · Computer Science 2022-07-19 Yi Li , Honghao Lin , David P. Woodruff , Yuheng Zhang

We identify a connection between the approximability of CSPs in two models: (i) sublinear space streaming algorithms, and (ii) the basic LP relaxation. We show that whenever the basic LP admits an integrality gap, there is an…

Computational Complexity · Computer Science 2025-09-23 Noah G. Singer , Madhur Tulsiani , Santhoshini Velusamy

Optimal transport is an important tool in machine learning, allowing to capture geometric properties of the data through a linear program on transport polytopes. We present a single-loop optimization algorithm for minimizing general convex…

Machine Learning · Computer Science 2023-06-21 Marin Ballu , Quentin Berthet

We give a deterministic 2^{O(n)} algorithm for computing an M-ellipsoid of a convex body, matching a known lower bound. This has several interesting consequences including improved deterministic algorithms for volume estimation of convex…

Computational Complexity · Computer Science 2014-03-05 Daniel Dadush , Santosh Vempala

Based on the characterization of the polyconvex envelope of isotropic functions by their signed singular value representations, we propose a simple algorithm for the numerical approximation of the polyconvex envelope. Instead of operating…

Numerical Analysis · Mathematics 2023-07-31 Timo Neumeier , Malte A. Peter , Daniel Peterseim , David Wiedemann

We describe a generalised method for ellipsoid fitting against a minimum set of data points. The proposed method is numerically stable and applies to a wide range of ellipsoidal shapes, including highly elongated and arbitrarily oriented…

Computer Vision and Pattern Recognition · Computer Science 2017-07-26 Amit Reza , Anand S. Sengupta

We present a deterministic $(1+\varepsilon)$-approximate maximum matching algorithm in $\mathsf{poly} 1/\varepsilon$ passes in the semi-streaming model, solving the long-standing open problem of breaking the exponential barrier in the…

Data Structures and Algorithms · Computer Science 2024-04-03 Manuela Fischer , Slobodan Mitrović , Jara Uitto

Low-rank approximation in data streams is a fundamental and significant task in computing science, machine learning and statistics. Multiple streaming algorithms have emerged over years and most of them are inspired by randomized…

Data Structures and Algorithms · Computer Science 2022-09-30 Cuiyu Liu , Chuanfu Xiao , Mingshuo Ding , Chao Yang

We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs…

Data Structures and Algorithms · Computer Science 2015-11-24 Ger Yang , Evdokia Nikolova

We adapt a well known streaming algorithm for approximating item frequencies to the matrix sketching setting. The algorithm receives the rows of a large matrix $A \in \R^{n \times m}$ one after the other in a streaming fashion. It maintains…

Data Structures and Algorithms · Computer Science 2012-07-12 Edo Liberty

We study streaming algorithms for Correlation Clustering. Given a graph as an arbitrary-order stream of edges, with each edge labeled as positive or negative, the goal is to partition the vertices into disjoint clusters, such that the…

Data Structures and Algorithms · Computer Science 2025-10-14 Yinhao Dong , Shan Jiang , Shi Li , Pan Peng