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Related papers: Range Reporting for Moving Points on a Grid

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We study the problem of $2$-dimensional orthogonal range counting with additive error. Given a set $P$ of $n$ points drawn from an $n\times n$ grid and an error parameter $\eps$, the goal is to build a data structure, such that for any…

Data Structures and Algorithms · Computer Science 2016-05-24 Zhewei Wei , Ke Yi

We consider a range-search variant of the closest-pair problem. Let $\varGamma$ be a fixed shape in the plane. We are interested in storing a given set of $n$ points in the plane in some data structure such that for any specified translate…

Computational Geometry · Computer Science 2019-03-25 Jie Xue , Yuan Li , Saladi Rahul , Ravi Janardan

We revisit the classic problem of simplex range searching and related problems in computational geometry. We present a collection of new results which improve previous bounds by multiple logarithmic factors that were caused by the use of…

Computational Geometry · Computer Science 2022-10-24 Timothy M. Chan , Da Wei Zheng

We present the first fully dynamic worst case I/O-efficient data structures that support planar orthogonal \textit{3-sided range skyline reporting queries} in $\bigO (\log_{2B^\epsilon} n + \frac{t}{B^{1-\epsilon}})$ I/Os and updates in…

Data Structures and Algorithms · Computer Science 2012-07-11 Casper Kejlberg-Rasmussen , Konstantinos Tsakalidis , Kostas Tsichlas

Given an array A of $n$ elements, we wish to support queries for the most frequent and least frequent element in a subrange $[l, r]$ of $A$. We also wish to support updates that change a particular element at index $i$ or insert/ delete an…

Data Structures and Algorithms · Computer Science 2018-07-12 Hicham El-Zein , Meng He , J. Ian Munro , Bryce Sandlund

A data structure, called a biased range tree, is presented that preprocesses a set S of n points in R^2 and a query distribution D for 2-sided orthogonal range counting queries. The expected query time for this data structure, when queries…

Computational Geometry · Computer Science 2008-06-18 Vida Dujmovic , John Howat , Pat Morin

We show that for any set of $n$ points moving along "simple" trajectories (i.e., each coordinate is described with a polynomial of bounded degree) in $\Re^d$ and any parameter $2 \le k \le n$, one can select a fixed non-empty subset of the…

Computational Geometry · Computer Science 2017-04-28 Jean-Lou De Carufel , Matya Katz , Matias Korman , André van Renssen , Marcel Roeloffzen , Shakhar Smorodinsky

Quantum walk has been successfully used to search for targets on graphs with vertices identified as the elements of a database. This spacial search on a two-dimensional periodic grid takes $\mathcal{O}\left(\sqrt{N\log N}\right)$ oracle…

Quantum Physics · Physics 2025-03-07 Pulak Ranjan Giri

The representation of subgrid-scale orography is a challenge in the physical parameterization of orographic gravity-wave sources in weather forecasting. A significant hurdle is encoding as much physical information with as simple a…

Atmospheric and Oceanic Physics · Physics 2025-01-16 Ray Chew , Stamen Dolaptchiev , Maja-Sophie Wedel , Ulrich Achatz

Let P be a set of n points in R^2. Given a rectangle Q = [\alpha_1, \alpha_2] x [\beta_1, \beta_2], a range skyline query returns the maxima of the points in P \cap Q. An important variant is the so-called top-open queries, where Q is a…

Data Structures and Algorithms · Computer Science 2013-07-17 Yufei Tao , Jeonghun Yoon

We propose to design data structures called succinct geometric indexes of negligible space (more precisely, o(n) bits) that, by taking advantage of the n points in the data set permuted and stored elsewhere as a sequence, to support…

Computational Geometry · Computer Science 2008-05-28 Prosenjit Bose , Eric Y. Chen , Meng He , Anil Maheshwari , Pat Morin

We study the point location problem on dynamic planar subdivisions that allows insertions and deletions of edges. In our problem, the underlying graph of a subdivision is not necessarily connected. We present a data structure of linear size…

Computational Geometry · Computer Science 2018-03-13 Eunjin Oh , Hee-Kap Ahn

Grid cells in the brain respond when an animal occupies a periodic lattice of "grid fields" during spatial navigation. The grid scale varies along the dorso-ventral axis of the entorhinal cortex. We propose that the grid system minimizes…

Neurons and Cognition · Quantitative Biology 2018-05-14 Xue-Xin Wei , Jason Prentice , Vijay Balasubramanian

We consider preprocessing a set $S$ of $n$ points in convex position in the plane into a data structure supporting queries of the following form: given a point $q$ and a directed line $\ell$ in the plane, report the point of $S$ that is…

Computational Geometry · Computer Science 2017-10-16 Boris Aronov , Prosenjit Bose , Erik D. Demaine , Joachim Gudmundsson , John Iacono , Stefan Langerman , Michiel Smid

This article proposes a new layered model to represent the spectrum assignment on flexible-grid optical networks. This model can reduce the time-complexity of existing routing and spectrum assignment methods by providing a data structure…

Networking and Internet Architecture · Computer Science 2015-12-14 Aysegul Yayimli

We revisit various string indexing problems with range reporting features, namely, position-restricted substring searching, indexing substrings with gaps, and indexing substrings with intervals. We obtain the following main results.…

Data Structures and Algorithms · Computer Science 2011-08-19 Philip Bille , Inge Li Goertz

We describe a data structure that can maintain a dynamic set of points given by their Cartesian coordinates, and maintain the point whose product of ranks within the two coordinate orderings is minimum or maximum, in time $O(\sqrt{n\log…

Computational Geometry · Computer Science 2020-07-17 David Eppstein

Given an array A[1: n] of n elements drawn from an ordered set, the sorted range selection problem is to build a data structure that can be used to answer the following type of queries efficiently: Given a pair of indices i, j $ (1\le i\le…

Data Structures and Algorithms · Computer Science 2025-04-22 Waseem Akram , Sanjeev Saxena

This paper sets a new foundation for data-driven inertial navigation research, where the task is the estimation of positions and orientations of a moving subject from a sequence of IMU sensor measurements. More concretely, the paper…

Computer Vision and Pattern Recognition · Computer Science 2019-05-31 Hang Yan , Sachini Herath , Yasutaka Furukawa

Temporal information plays a crucial role in many database applications, however support for queries on such data is limited. We present an index structure, termed RD-index, to support range-duration queries over interval timestamped…

Databases · Computer Science 2022-06-16 Matteo Ceccarello , Anton Dignös , Johann Gamper , Christina Khnaisser