Related papers: Simpler is Faster: Practical Distance Reporting by…
We perform experimental studies on data structures that answer path median, path counting, and path reporting queries in weighted trees. These query problems generalize the well-known range median query problem in arrays, as well as the…
The range, segment and rectangle query problems are fundamental problems in computational geometry, and have extensive applications in many domains. Despite the significant theoretical work on these problems, efficient implementations can…
We initiate a study of a query-driven approach to designing partition trees for range-searching problems. Our model assumes that a data structure is to be built for an unknown query distribution that we can access through a sampling oracle,…
In a typical range emptiness searching (resp., reporting) problem, we are given a set $P$ of $n$ points in $\reals^d$, and wish to preprocess it into a data structure that supports efficient range emptiness (resp., reporting) queries, in…
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 $S$…
In the orthogonal range reporting problem we must pre-process a set $P$ of multi-dimensional points, so that for any axis-parallel query rectangle $q$ all points from $q\cap P$ can be reported efficiently. In this paper we study the query…
In this paper we consider a variant of the orthogonal range reporting problem when all points should be reported in the sorted order of their $x$-coordinates. We show that reporting two-dimensional points with this additional condition can…
We study the Fr\'echet queries problem. It is a data structure problem, where we are given a set $S$ of $n$ polygonal curves and a distance threshold $\rho$. The data structure should support queries with a polygonal curve $q$ for the…
We study the following range searching problem in high-dimensional Euclidean spaces: given a finite set $P\subset \mathbb{R}^d$, where each $p\in P$ is assigned a weight $w_p$, and radius $r>0$, we need to preprocess $P$ into a data…
Range closest-pair (RCP) search is a range-search variant of the classical closest-pair problem, which aims to store a given set $S$ of points into some space-efficient data structure such that when a query range $Q$ is specified, the…
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.…
Given a dataset $S$ of points in $\mathbb{R}^2$, the range closest-pair (RCP) problem aims to preprocess $S$ into a data structure such that when a query range $X$ is specified, the closest-pair in $S \cap X$ can be reported efficiently.…
Traditional problems in computational geometry involve aspects that are both discrete and continuous. One such example is nearest-neighbor searching, where the input is discrete, but the result depends on distances, which vary continuously.…
Efficient processing of aggregated range queries on two-dimensional grids is a common requirement in information retrieval and data mining systems, for example in Geographic Information Systems and OLAP cubes. We introduce a technique to…
In this paper we describe a new data structure that supports orthogonal range reporting queries on a set of points that move along linear trajectories on a $U\times U$ grid. The assumption that points lie on a $U\times U$ grid enables us to…
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…
We propose an extension of tree-based space-partitioning indexing structures for data with low intrinsic dimensionality embedded in a high dimensional space. We call this extension an Angle Tree. Our extension can be applied to both…
We consider the two-dimensional sorted range reporting problem. Our data structure requires O(n lglg n) words of space and O(lglg n + k lglg n) query time, where k is the number of points in the query range. This data structure improves a…
We consider the problem of reporting convex hull points in an orthogonal range query in two dimensions. Formally, let $P$ be a set of $n$ points in $\mathbb{R}^{2}$. A point lies on the convex hull of a point set $S$ if it lies on the…
We describe a data structure, called a priority range tree, which accommodates fast orthogonal range reporting queries on prioritized points. Let $S$ be a set of $n$ points in the plane, where each point $p$ in $S$ is assigned a weight…