Related papers: A Practical Approach for Computing the Diameter of…
We consider the directed Hausdorff distance between point sets in the plane, where one or both point sets consist of imprecise points. An imprecise point is modelled by a disc given by its centre and a radius. The actual position of an…
We present a new algorithm for estimating the star discrepancy of arbitrary point sets. Similar to the algorithm for discrepancy approximation of Winker and Fang [SIAM J. Numer. Anal. 34 (1997), 2028--2042] it is based on the optimization…
Computer experiments with quantitative and qualitative inputs are widely used to study many scientific and engineering processes. Much of the existing work has focused on design and modeling or process optimization for such experiments.…
In this paper we consider the fundamental problem of approximating the diameter $D$ of directed or undirected graphs. In a seminal paper, Aingworth, Chekuri, Indyk and Motwani [SIAM J. Comput. 1999] presented an algorithm that computes in…
$\newcommand{\popt}{{\mathcal{p}}} \newcommand{\Re}{\mathbb{R}}\newcommand{\N}{{\mathcal{N}}} \newcommand{\BX}{\mathcal{B}} \newcommand{\bb}{\mathsf{b}} \newcommand{\eps}{\varepsilon} \newcommand{\polylog}{\mathrm{polylog}} $ Let…
We describe two quantum algorithms to approximate the mean value of a black-box function. The first algorithm is novel and asymptotically optimal while the second is a variation on an earlier algorithm due to Aharonov. Both algorithms have…
Let $\RR$ be a real closed field (e.g. the field of real numbers) and $\mathscr{S} \subset \RR^n$ be a semi-algebraic set defined as the set of points in $\RR^n$ satisfying a system of $s$ equalities and inequalities of multivariate…
A simple, analytically correct algorithm is developed for calculating pencil beam coordinates using the signals from an ideal cylindrical particle beam position monitor (BPM) with four pickup electrodes (PUEs) of infinitesimal widths. The…
Over the past a few years, research and development has made significant progresses on big data analytics. A fundamental issue for big data analytics is the efficiency. If the optimal solution is unable to attain or not required or has a…
The diameter, radius and eccentricities are natural graph parameters. While these problems have been studied extensively, there are no known dynamic algorithms for them beyond the ones that follow from trivial recomputation after each…
The construction of $r$-nets offers a powerful tool in computational and metric geometry. We focus on high-dimensional spaces and present a new randomized algorithm which efficiently computes approximate $r$-nets with respect to Euclidean…
First, we study geometric variants of the standard set cover motivated by assignment of directional antenna and shipping with deadlines, providing the first known polynomial-time exact solutions. Next, we consider the following general…
We present a new algorithm for reconstructing an exact algebraic number from its approximate value using an improved parameterized integer relation construction method. Our result is consistent with the existence of error controlling on…
We present a new object representation, called Dense RepPoints, that utilizes a large set of points to describe an object at multiple levels, including both box level and pixel level. Techniques are proposed to efficiently process these…
Generalized matrix approximation plays a fundamental role in many machine learning problems, such as CUR decomposition, kernel approximation, and matrix low rank approximation. Especially with today's applications involved in larger and…
It is a common contention that it is an ``impossible mission'' to exactly determine the minimum sample size for the estimation of a binomial parameter with prescribed margin of error and confidence level. In this paper, we investigate such…
Convex hulls are fundamental objects in computational geometry. In moderate dimensions or for large numbers of vertices, computing the convex hull can be impractical due to the computational complexity of convex hull algorithms. In this…
We develop a new algorithm for fitting circles that does not have drawbacks commonly found in existing circle fits. Our fit achieves ultimate accuracy (to machine precision), avoids divergence, and is numerically stable even when fitting…
We study computing geometric problems on uncertain points. An uncertain point is a point that does not have a fixed location, but rather is described by a probability distribution. When these probability distributions are restricted to a…
We develop fixed-point algorithms for the approximation of structured matrices with rank penalties. In particular we use these fixed-point algorithms for making approximations by sums of exponentials, or frequency estimation. For the basic…