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Modern tracking technology has made the collection of large numbers of densely sampled trajectories of moving objects widely available. We consider a fundamental problem encountered when analysing such data: Given $n$ polygonal curves $S$…

Computational Geometry · Computer Science 2017-07-18 Peyman Afshani , Anne Driemel

We study the convex-hull problem in a probabilistic setting, motivated by the need to handle data uncertainty inherent in many applications, including sensor databases, location-based services and computer vision. In our framework, the…

Computational Geometry · Computer Science 2014-06-26 Pankaj K. Agarwal , Sariel Har-Peled , Subhash Suri , Hakan Yildiz , Wuzhou Zhang

Motivated by the mode estimation problem of an unknown multivariate probability density function, we study the problem of identifying the point with the minimum k-th nearest neighbor distance for a given dataset of n points. We study the…

Machine Learning · Statistics 2020-10-27 Anirudh Singhal , Subham Pirojiwala , Nikhil Karamchandani

$\newcommand{\dist}{\operatorname{dist}}$ In this paper we define the notion of a probabilistic neighborhood in spatial data: Let a set $P$ of $n$ points in $\mathbb{R}^d$, a query point $q \in \mathbb{R}^d$, a distance metric $\dist$, and…

Data Structures and Algorithms · Computer Science 2016-08-17 Moritz von Looz , Henning Meyerhenke

We investigate determining the exact bounds of the frequencies of conjunctions based on frequent sets. Our scenario is an important special case of some general probabilistic logic problems that are known to be intractable. We show that…

Computational Complexity · Computer Science 2019-02-05 Nikolaj Tatti

In this paper, we consider the rectilinear one-center problem on uncertain points in the plane. In this problem, we are given a set $P$ of $n$ (weighted) uncertain points in the plane and each uncertain point has $m$ possible locations each…

Computational Geometry · Computer Science 2015-09-18 Haitao Wang , Jingru Zhang

For a set of $n$ points in $\Re^d$, and parameters $k$ and $\eps$, we present a data structure that answers $(1+\eps,k)$-\ANN queries in logarithmic time. Surprisingly, the space used by the data-structure is $\Otilde (n /k)$; that is, the…

Computational Geometry · Computer Science 2013-04-10 Sariel Har-Peled , Nirman Kumar

The need for scalable concurrent ordered set data structures with linearizable range query support is increasing due to the rise of multicore computers, data processing platforms and in-memory databases. This paper presents a new concurrent…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-09-05 Kjell Winblad

We study problems with stochastic uncertainty information on intervals for which the precise value can be queried by paying a cost. The goal is to devise an adaptive decision tree to find a correct solution to the problem in consideration…

Data Structures and Algorithms · Computer Science 2021-09-27 Steven Chaplick , Magnús M. Halldórsson , Murilo S. de Lima , Tigran Tonoyan

Top-$k$ queries allow end-users to focus on the most important (top-$k$) answers amongst those which satisfy the query. In traditional databases, a user defined score function assigns a score value to each tuple and a top-$k$ query returns…

Databases · Computer Science 2010-07-30 Manish Patil , Rahul Shah , Sharma V. Thankachan

This paper is concerned with the density of rational points of bounded height lying on a variety defined by an integral quadratic form Q. In the case of four variables, we give an estimate that does not depend on the coefficients of Q. For…

Number Theory · Mathematics 2020-03-31 Félicien Comtat

We consider here the problem of obtaining reliable, consistent information from inconsistent databases -- databases that do not have to satisfy given integrity constraints. We use the notion of consistent query answer -- a query answer…

Databases · Computer Science 2007-05-23 Jan Chomicki , Jerzy Marcinkowski

Given an array A containing arbitrary (positive and negative) numbers, we consider the problem of supporting range maximum-sum segment queries on A: i.e., given an arbitrary range [i,j], return the subrange [i' ,j' ] \subseteq [i,j] such…

Data Structures and Algorithms · Computer Science 2015-06-12 Pawel Gawrychowski , Patrick K. Nicholson

We study how to utilize (possibly erroneous) predictions in a model for computing under uncertainty in which an algorithm can query unknown data. Our aim is to minimize the number of queries needed to solve the minimum spanning tree…

Data Structures and Algorithms · Computer Science 2022-07-01 Thomas Erlebach , Murilo Santos de Lima , Nicole Megow , Jens Schlöter

Let $G$ be a (possibly disconnected) planar subdivision and let $D$ be a probability measure over $\R^2$. The current paper shows how to preprocess $(G,D)$ into an O(n) size data structure that can answer planar point location queries over…

Computational Geometry · Computer Science 2010-01-18 Prosenjit Bose , Luc Devroye , Karim Douieb , Vida Dujmovic , James King , Pat Morin

Quantum computing is a popular topic in computer science, which has recently attracted many studies in various areas such as machine learning and network. However, the topic of quantum data structures seems neglected. There is an open…

Databases · Computer Science 2024-06-03 Hao Liu , Xiaotian You , Raymond Chi-Wing Wong

Range Minimum Query (RMQ) is an important building brick of many compressed data structures and string matching algorithms. Although this problem is essentially solved in theory, with sophisticated data structures allowing for constant time…

Data Structures and Algorithms · Computer Science 2017-11-29 Tomasz Kowalski , Szymon Grabowski

We have investigated how uncertainties in the estimation of the detection efficiency affect the 90% confidence intervals in the unified approach for constructing confidence intervals. The study has been conducted for experiments where the…

Nuclear Experiment · Physics 2009-06-10 E. S. Smith

A typical computational geometry problem begins: Consider a set P of n points in R^d. However, many applications today work with input that is not precisely known, for example when the data is sensed and has some known error model. What if…

Computational Geometry · Computer Science 2008-12-17 Maarten Loffler , Jeff M. Phillips

Given a metric space, a standard metric range search, given a query $(q,r)$, finds all points within distance $r$ of the point $q$. Suppose now we have two different metrics $d_1$ and $d_2$. A product range query $(q, r_1, r_2)$ is a point…

Computational Geometry · Computer Science 2026-03-25 Oliver Chubet , Niyathi Kukkapalli , Anvi Kudaraya , Don Sheehy