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Given a set $S$ of $n$ points in $\mathbb{R}^d$, the Closest Pair problem is to find a pair of distinct points in $S$ at minimum distance. When $d$ is constant, there are efficient algorithms that solve this problem, and fast approximate…
We establish new exponential in dimension lower bounds for the Maximum Halfspace Discrepancy problem, which models linear classification. Both are fundamental problems in computational geometry and machine learning in their exact and…
We consider the problem of designing a succinct data structure for {\it path graphs} (which are a proper subclass of chordal graphs and a proper superclass of interval graphs) on $n$ vertices while supporting degree, adjacency, and…
We initiate a study of solving a row/column diagonally dominant (RDD/CDD) linear system $Mx=b$ in sublinear time, with the goal of estimating $t^{\top}x^*$ for a given vector $t\in R^n$ and a specific solution $x^*$. This setting naturally…
We propose a new approach to represent nonparametrically the linear dependence structure of a spatio-temporal process in terms of latent common factors. Though it is formally similar to the existing reduced rank approximation methods…
We propose a data structure in $d$-dimensional hyperbolic space that can be considered a natural counterpart to quadtrees in Euclidean spaces. Based on this data structure we propose a so-called L-order for hyperbolic point sets, which is…
The width measure treedepth, also known as vertex ranking, centered coloring and elimination tree height, is a well-established notion which has recently seen a resurgence of interest. Since graphs of bounded treedepth are more restricted…
We consider various data-analysis queries on two-dimensional points. We give new space/time tradeoffs over previous work on geometric queries such as dominance and rectangle visibility, and on semigroup and group queries such as sum,…
Given an $n$-vertex planar embedded digraph $G$ with non-negative edge weights and a face $f$ of $G$, Klein presented a data structure with $O(n\log n)$ space and preprocessing time which can answer any query $(u,v)$ for the shortest path…
We revisit the range sampling problem: the input is a set of points where each point is associated with a real-valued weight. The goal is to store them in a structure such that given a query range and an integer $k$, we can extract $k$…
We consider the problem of computing a sequence of range minimum queries. We assume a sequence of commands that contains values and queries. Our goal is to quickly determine the minimum value that exists between the current position and a…
Many NP-hard problems, such as Dominating Set, are FPT parameterized by clique-width. For graphs of clique-width $k$ given with a $k$-expression, Dominating Set can be solved in $4^k n^{O(1)}$ time. However, no FPT algorithm is known for…
Bille and G{\o}rtz (2011) recently introduced the problem of substring range counting, for which we are asked to store compactly a string $S$ of $n$ characters with integer labels in ([0, u]), such that later, given an interval ([a, b]) and…
Supporting top-k document retrieval queries on general text databases, that is, finding the k documents where a given pattern occurs most frequently, has become a topic of interest with practical applications. While the problem has been…
Given an array of distinct integers $A[1\ldots n]$, the Range Minimum Query (RMQ) problem requires us to construct a data structure from $A$, supporting the RMQ query: given an interval $[a,b]\subseteq[1,n]$, return the index of the minimum…
In the last decades, the necessity to process massive amounts of textual data fueled the development of compressed text indexes: data structures efficiently answering queries on a given text while occupying space proportional to the…
We develop, analyze, implement, and compare new algorithms for creating $\varepsilon$-samples of range spaces defined by halfspaces which have size sub-quadratic in $1/\varepsilon$, and have runtime linear in the input size and…
Understanding the relationships between data points in the latent decision space derived by the deep learning system is critical to evaluating and interpreting the performance of the system on real world data. Detecting…
Let $P$ be a set of $n$ points in ${\mathbb R}^{d}$. A point $p \in P$ is $k$\emph{-shallow} if it lies in a halfspace which contains at most $k$ points of $P$ (including $p$). We show that if all points of $P$ are $k$-shallow, then $P$ can…
In this paper, we study the dominating set problem in \emph{RDV graphs}, a graph class that lies between interval graphs and chordal graphs and is defined as the \textbf{v}ertex-intersection graphs of \textbf{d}ownward paths in a…