Related papers: Streaming Euclidean Max-Cut: Dimension vs Data Red…
We seek to augment a geometric network in the Euclidean plane with shortcuts to minimize its continuous diameter, i.e., the largest network distance between any two points on the augmented network. Unlike in the discrete setting where a…
The streaming model of computation is a popular approach for working with large-scale data. In this setting, there is a stream of items and the goal is to compute the desired quantities (usually data statistics) while making a single pass…
Current structural pruning methods face two significant limitations: (i) they often limit pruning to finer-grained levels like channels, making aggressive parameter reduction challenging, and (ii) they focus heavily on parameter and FLOP…
In an era where big and high-dimensional data is readily available, data scientists are inevitably faced with the challenge of reducing this data for expensive downstream computation or analysis. To this end, we present here a new method…
Consider a set $P$ of $n$ points in $\mathbb{R}^d$. In the discrete median line segment problem, the objective is to find a line segment bounded by a pair of points in $P$ such that the sum of the Euclidean distances from $P$ to the line…
The Maximum Cut (MaxCut) problem is NP-Complete, and obtaining its optimal solution is NP-hard in the worst case. As a result, heuristic-based algorithms are commonly used, though their design often requires significant domain expertise.…
We consider the Max Unique Coverage problem, including applications to the data stream model. The input is a universe of $n$ elements, a collection of $m$ subsets of this universe, and a cardinality constraint, $k$. The goal is to select a…
We consider streaming algorithms for approximating a product of input probabilities up to multiplicative error of $1-\epsilon$. It is shown that every randomized streaming algorithm for this problem needs space $\Omega(\log n + \log b -…
Many practical prediction algorithms represent inputs in Euclidean space and replace the discrete 0/1 classification loss with a real-valued surrogate loss, effectively reducing classification tasks to stochastic optimization. In this…
Trevisan [SICOMP 2012] presented an algorithm for Max-Cut based on spectral partitioning techniques. This is the first algorithm for Max-Cut with an approximation guarantee strictly larger than 1/2 that is not based on semidefinite…
Continual learning aims to efficiently learn from a non-stationary stream of data while avoiding forgetting the knowledge of old data. In many practical applications, data complies with non-Euclidean geometry. As such, the commonly used…
Interactive exploration of large, multidimensional datasets plays a very important role in various scientific fields. It makes it possible not only to identify important structural features and forms, such as clusters of vertices and their…
We study the min-max optimization problem where each function contributing to the max operation is strongly-convex and smooth with bounded gradient in the search domain. By smoothing the max operator, we show the ability to achieve an…
We study metric data structures for curves in doubling spaces, such as trajectories of moving objects in Euclidean $\mathbb{R}^d$, where the distance between two curves is measured using the discrete Fr\'echet distance. We design data…
The arrangement of network nodes in hyperbolic spaces has become a widely studied problem, motivated by numerous results suggesting the existence of hidden metric spaces behind the structure of complex networks. Although several methods…
We present a dimensionally split method for solving hyperbolic conservation laws on Cartesian cut cell meshes. The approach combines local geometric and wave speed information to determine a novel stabilised cut cell flux, and we provide a…
We study high-dimensional robust statistics tasks in the streaming model. A recent line of work obtained computationally efficient algorithms for a range of high-dimensional robust estimation tasks. Unfortunately, all previous algorithms…
A fundamental question in many data analysis settings is the problem of discerning the "natural" dimension of a data set. That is, when a data set is drawn from a manifold (possibly with noise), a meaningful aspect of the data is the…
Classical multidimensional scaling only works well when the noisy distances observed in a high dimensional space can be faithfully represented by Euclidean distances in a low dimensional space. Advanced models such as Maximum Variance…
In binary images, the distance transformation (DT) and the geometrical skeleton extraction are classic tools for shape analysis. In this paper, we present time optimal algorithms to solve the reverse Euclidean distance transformation and…