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An $\varepsilon$-coreset for Least-Mean-Squares (LMS) of a matrix $A\in{\mathbb{R}}^{n\times d}$ is a small weighted subset of its rows that approximates the sum of squared distances from its rows to every affine $k$-dimensional subspace of…
The computational complexity of the self-attention mechanism in popular transformer architectures poses significant challenges for training and inference, and becomes the bottleneck for long inputs. Is it possible to significantly reduce…
This paper introduces a new algorithm for the fundamental problem of generating a random integer from a discrete probability distribution using a source of independent and unbiased random coin flips. We prove that this algorithm, which we…
In numerical linear algebra, considerable effort has been devoted to obtaining faster algorithms for linear systems whose underlying matrices exhibit structural properties. A prominent success story is the method of generalized nested…
The computational workload involved in Convolutional Neural Networks (CNNs) is typically out of reach for low-power embedded devices. There are a large number of approximation techniques to address this problem. These methods have…
We present a family of fast pseudo-approximation algorithms for the minimum balanced vertex separator problem in a graph. Given a graph $G=(V,E)$ with $n$ vertices and $m$ edges, and a (constant) balance parameter $c\in(0,1/2)$, where $G$…
We significantly improve known time bounds for solving the minimum cut problem on undirected graphs. We use a ``semi-duality'' between minimum cuts and maximum spanning tree packings combined with our previously developed random sampling…
The extraction of k-mers from sequencing reads is an important task in many bioinformatics applications, such as all DNA sequence analysis methods based on de Bruijn graphs. These methods tend to be more accurate when the used k-mers are…
Despite the prevalence and many successes of deep learning applications in de novo molecular design, the problem of peptide generation targeting specific proteins remains unsolved. A main barrier for this is the scarcity of the high-quality…
We study the classic set cover problem from the perspective of sub-linear algorithms. Given access to a collection of $m$ sets over $n$ elements in the query model, we show that sub-linear algorithms derived from existing techniques have…
A combinatorial design is a family of sets that are almost disjoint, which is applied in pseudo random number generations and randomness extractions. The parameter, $\rho$, quantifying the overlap between the sets within the family, is…
The approximate single-source shortest-path problem is as follows: given a graph with nonnegative edge weights and a designated source vertex $s$, return estimates of the distances from~$s$ to each other vertex such that the estimate falls…
Unbreakable decomposition, introduced by Cygan et al. (SICOMP'19) and Cygan et al. (TALG'20), has proven to be one of the most powerful tools for parameterized graph cut problems in recent years. Unfortunately, all known constructions…
Minimum-weight cut (min-cut) is a basic measure of a network's connectivity strength. While the min-cut can be computed efficiently in the sequential setting [Karger STOC'96], there was no efficient way for a distributed network to compute…
In recent years, significant progress has been made in explaining the apparent hardness of improving upon the naive solutions for many fundamental polynomially solvable problems. This progress has come in the form of conditional lower…
We consider the minimum cut problem in undirected, weighted graphs. We give a simple algorithm to find a minimum cut that $2$-respects (cuts two edges of) a spanning tree $T$ of a graph $G$. This procedure can be used in place of the…
We study a game theoretic model where a coalition of processors might collude to bias the outcome of the protocol, where we assume that the processors always prefer any legitimate outcome over a non-legitimate one. We show that the problems…
We study the fundamental problem of high-dimensional mean estimation in a robust model where a constant fraction of the samples are adversarially corrupted. Recent work gave the first polynomial time algorithms for this problem with…
We consider $N$-way data arrays and low-rank tensor factorizations where the time mode is coded as a sparse linear combination of temporal elements from an over-complete library. Our method, Shape Constrained Tensor Decomposition (SCTD) is…
We study the problem of learning Bayesian networks where an $\epsilon$-fraction of the samples are adversarially corrupted. We focus on the fully-observable case where the underlying graph structure is known. In this work, we present the…