Related papers: Dynamic Range Selection in Linear Space
We revisit the range minimum query problem and present a new O(n)-space data structure that supports queries in O(1) time. Although previous data structures exist whose asymptotic bounds match ours, our goal is to introduce a new solution…
Given a set $P$ of coloured points on the real line, we study the problem of answering range $\alpha$-majority (or "heavy hitter") queries on $P$. More specifically, for a query range $Q$, we want to return each colour that is assigned to…
For a set $P$ of $n$ points in the plane and a value $r > 0$, the unit-disk range reporting problem is to construct a data structure so that given any query disk of radius $r$, all points of $P$ in the disk can be reported efficiently. We…
In this paper we present new data structures for two extensively studied variants of the orthogonal range searching problem. First, we describe a data structure that supports two-dimensional orthogonal range minima queries in $O(n)$ space…
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 present a data-structure for orthogonal range searching for random points in the plane. The new data-structure uses (in expectation) $O\bigl(n \log n ( \log \log n)^2 \bigr)$ space, and answers emptiness queries in constant time. As a…
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…
We give a simplified and improved lower bound for the simplex range reporting problem. We show that given a set $P$ of $n$ points in $\mathbb{R}^d$, any data structure that uses $S(n)$ space to answer such queries must have…
We consider succinct data structures for representing a set of $n$ horizontal line segments in the plane given in rank space to support \emph{segment access}, \emph{segment selection}, and \emph{segment rank} queries. A segment access query…
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…
For any $\epsilon \in (0,1)$, a $(1+\epsilon)$-approximate range mode query asks for the position of an element whose frequency in the query range is at most a factor $(1+\epsilon)$ smaller than the true mode. For this problem, we design an…
A mode of a multiset $S$ is an element $a \in S$ of maximum multiplicity; that is, $a$ occurs at least as frequently as any other element in $S$. Given a list $A[1:n]$ of $n$ items, we consider the problem of constructing a data structure…
We revisit the range sampling problem: the input is a set of points where each point is associated with a real-valued weight. The goal is to store them in a structure such that given a query range and an integer $k$, we can extract $k$…
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 $S$…
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…
Given a set $P$ of $n$ uncertain points on the real line, each represented by its one-dimensional probability density function, we consider the problem of building data structures on $P$ to answer range queries of the following three types…
We consider the problem of computing a sequence of range minimum queries. We assume a sequence of commands that contains values and queries. Our goal is to quickly determine the minimum value that exists between the current position and a…
In the dynamic range mode problem, we are given a sequence $a$ of length bounded by $N$ and asked to support element insertion, deletion, and queries for the most frequent element of a contiguous subsequence of $a$. In this work, we devise…
Given a set $P$ of $n$ points in the plane, we consider the problem of computing the number of points of $P$ in a query unit disk (i.e., all query disks have the same radius). We show that the main techniques for simplex range searching in…
Given a string $S$ of $n$ integers in $[0,\sigma)$, a range minimum query RMQ$(i, j)$ asks for the index of the smallest integer in $S[i \dots j]$. It is well known that the problem can be solved with a succinct data structure of size $2n +…