Related papers: On ultrametric $1$-median selection

We investigate the properties of a sequential Monte Carlo method where the particle weight that appears in the algorithm is estimated by a positive, unbiased estimator. We present broadly-applicable convergence results, including a central…

Given point sets $A$ and $B$ in $\mathbb{R}^d$ where $A$ and $B$ have equal size $n$ for some constant dimension $d$ and a parameter $\varepsilon>0$, we present the first deterministic algorithm that computes, in $n\cdot(\varepsilon^{-1}…

In this paper we are interested in indexing texts for substring matching queries with one edit error. That is, given a text $T$ of $n$ characters over an alphabet of size $\sigma$, we are asked to build a data structure that answers the…

Finding an exact maximum distance of two points in the given set is a fundamental computational problem which is solved in many applications. This paper presents a fast, simple to implement and robust algorithm for finding this maximum…

We consider the planar Euclidean two-center problem in which given $n$ points in the plane we are to find two congruent disks of the smallest radius covering the points. We present a deterministic $O(n \log n)$-time algorithm for the case…

This project investigates the applicability of quasi-Monte Carlo methods to Euclidean lattice systems in order to improve the asymptotic error scaling of observables for such theories. The error of an observable calculated by averaging over…

For each $p \in (0,2]$, we present a randomized algorithm that returns an $\epsilon$-approximation of the $p$th frequency moment of a data stream $F_p = \sum_{i = 1}^n \abs{f_i}^p$. The algorithm requires space $O(\epsilon^{-2} \log…

This paper presents a distributed O(1)-approximation algorithm, with expected-$O(\log \log n)$ running time, in the $\mathcal{CONGEST}$ model for the metric facility location problem on a size-$n$ clique network. Though metric facility…

The proof of the theorem, which states that the Euclidean metric on the set of random points in an $n$-dimensional Euclidean space with the distribution of a special class, converges in probability in the limit $n\rightarrow\infty$ to the…

Given a point set P in 2D, the problem of finding the smallest set of unit disks that cover all of P is NP-hard. We present a simple algorithm for this problem with an approximation factor of 25/6 in the Euclidean norm and 2 in the max…

On sparse graphs, Roditty and Williams [2013] proved that no $O(n^{2-\varepsilon})$-time algorithm achieves an approximation factor smaller than $\frac{3}{2}$ for the diameter problem unless SETH fails. In this article, we solve an open…

We study the problem of minimum enclosing rectangle with outliers, which asks to find, for a given set of $n$ planar points, a rectangle with minimum area that encloses at least $(n-t)$ points. The uncovered points are regarded as outliers.…

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…

The $k$-means problem is a classic objective for modeling clustering in a metric space. Given a set of points in a metric space, the goal is to find $k$ representative points so as to minimize the sum of the squared distances from each…

We describe an embarrassingly parallel, anytime Monte Carlo method for likelihood-free models. The algorithm starts with the view that the stochasticity of the pseudo-samples generated by the simulator can be controlled externally by a…

In a spherically complete ultrametric space, a strictly contracting mapping has a fixed point. We indicate in this paper how this fixed point can either be reached or approximated.

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…

Monte Carlo integration is a commonly used technique to compute intractable integrals and is typically thought to perform poorly for very high-dimensional integrals. To show that this is not always the case, we examine Monte Carlo…

Let $X$ be a set of $n$ points of norm at most $1$ in the Euclidean space $R^k$, and suppose $\varepsilon>0$. An $\varepsilon$-distance sketch for $X$ is a data structure that, given any two points of $X$ enables one to recover the square…

In algorithms for finite metric spaces, it is common to assume that the distance between two points can be computed in constant time, and complexity bounds are expressed only in terms of the number of points of the metric space. We…