We present a succinct representation of a set of n points on an n × n grid using n lg n + o(n lg n) bits to support orthogonal range counting in O(lg n/ lg lg n) time, and range reporting in O(k lg n/ lg lg n) time, where k is the size of the output. This achieves an improvement on query time by a factor of lg lg n upon the previous result of Mäkinen and Navarro [1], while using essentially the...

We present the first adaptive data structure for two-dimensional orthogonal range search. Our data structure is adaptive in the sense that it gives improved search performance for data with more inherent sortedness. Given n points in the plane, it can answer range queries in O(k logn+m) time, where m is the number of points in the output and k is the minimum number of monotonic chains into whic...

We study the problem of 2-dimensional orthogonal range counting with additive error. Given a set P of n points drawn from an n× n grid and an error parameter ε, the goal is to build a data structure, such that for any orthogonal range R, the data structure can return the number of points in P ∩ R with additive error εn. A well-known solution for this problem is the εapproximation. Informally sp...

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 that is simple, intuitive, and practical without increasing asymptotic costs for query time or space.

Die zunehmende Bedeutung von Graphdaten im Kontext von Big Data erfordert wirksame Verfahren zur Erkennung von Duplikaten, d. h. Knoten, welche das selbe Realweltobjekt repräsentieren. Dieser Beitrag stellt die Integration von Techniken zur Duplikaterkennung innerhalb des Graphverarbeitungs-Frameworks GRADOOP vor. Dazu werden dem GRADOOP-Framework neue Operatoren zur Duplikaterkennung hinzugefü...

A range query on a set of points in a k-dimensional coordinate space asks for all points lying within a hyperrectangle specified by ranges of permissible values for each of the coordinates. In this paper we regard as identical any two range queries which return the same set of points. We then Investigate the number of range queries possible on a set—given a set of N points in k-space, what Is t...

In this paper we describe data structures for orthogonal range reporting in external memory that support fast update operations. The query costs either match the query costs of the best previously known data structures or differ by a small multiplicative factor.