Related papers: Computing Bi-Lipschitz Outlier Embeddings into the…

An $\ell_p$ oblivious subspace embedding is a distribution over $r \times n$ matrices $\Pi$ such that for any fixed $n \times d$ matrix $A$, $$\Pr_{\Pi}[\textrm{for all }x, \ \|Ax\|_p \leq \|\Pi Ax\|_p \leq \kappa \|Ax\|_p] \geq 9/10,$$…

This paper studies the minimal dimension required to embed subset memberships ($m$ elements and ${m\choose k}$ subsets of at most $k$ elements) into vector spaces, denoted as Minimal Embeddable Dimension (MED). The tight bounds of MED are…

An $\epsilon$-approximate incidence between a point and some geometric object (line, circle, plane, sphere) occurs when the point and the object lie at distance at most $\epsilon$ from each other. Given a set of points and a set of objects,…

The Ollivier curvature has important applications in discrete geometry and network theory, in particular as a measure of local clustering. The Ollivier curvature is defined in terms of the Wasserstein distance which, in the discrete…

Many geometric optimization problems can be reduced to finding points in space (centers) minimizing an objective function which continuously depends on the distances from the centers to given input points. Examples are $k$-Means, Geometric…

The Johnson-Lindenstrauss lemma is a fundamental result in probability with several applications in the design and analysis of algorithms in high dimensional geometry. Most known constructions of linear embeddings that satisfy the…

The problem of computing an exact experimental design that is optimal for the least-squares estimation of the parameters of a regression model is considered. We show that this problem can be solved via mixed-integer linear programming…

The main question studied in this article may be viewed as a nonlinear analogue of Dvoretzky's theorem in Banach space theory or as part of Ramsey theory in combinatorics. Given a finite metric space on n points, we seek its subspace of…

$\renewcommand{\Re}{\mathbb{R}}$ We develop a general randomized technique for solving "implic it" linear programming problems, where the collection of constraints are defined implicitly by an underlying ground set of elements. In many…

The presence of outliers can significantly degrade the performance of ellipse fitting methods. We develop an ellipse fitting method that is robust to outliers based on the maximum correntropy criterion with variable center (MCC-VC), where a…

Given a metric space $(X,d)$, a set of terminals $K\subseteq X$, and a parameter $t\ge 1$, we consider metric structures (e.g., spanners, distance oracles, embedding into normed spaces) that preserve distances for all pairs in $K\times X$…

In this work, we study the classic submodular maximization problem under knapsack constraints and beyond. We first present an $(7/16-\varepsilon)$-approximate algorithm for single knapsack constraint, which requires…

We prove that given a discrete space with $n$ points which is either embedded in a system of $k$ trees, or the Cartesian product of $k$ trees, we can compute all eccentricities in ${\cal O}(2^{{\cal O}(k\log{k})}(N+n)^{1+o(1)})$ time, where…

We consider the classic Facility Location, $k$-Median, and $k$-Means problems in metric spaces of doubling dimension $d$. We give nearly linear-time approximation schemes for each problem. The complexity of our algorithms is…

We obtain a characterization on self-orthogonality for a given binary linear code in terms of the number of column vectors in its generator matrix, which extends the result of Bouyukliev et al. (2006). As an application, we give an…

The seminal result of Johnson and Lindenstrauss on random embeddings has been intensively studied in applied and theoretical computer science. Despite that vast body of literature, we still lack of complete understanding of statistical…

We suggest a new optimization technique for minimizing the sum $\sum_{i=1}^n f_i(x)$ of $n$ non-convex real functions that satisfy a property that we call piecewise log-Lipschitz. This is by forging links between techniques in computational…

In a seminal paper on finding large matchings in sparse random graphs, Karp and Sipser proposed two algorithms for this task. The second algorithm has been intensely studied, but due to technical difficulties, the first algorithm has…

This paper introduces an algorithm to select demonstration examples for in-context learning of a query set. Given a set of $n$ examples, how can we quickly select $k$ out of $n$ to best serve as the conditioning for downstream inference?…

We revisit the problem of maintaining the longest increasing subsequence (LIS) of an array under (i) inserting an element, and (ii) deleting an element of an array. In a recent breakthrough, Mitzenmacher and Seddighin [STOC 2020] designed…