Related papers: Optimal Planar Range Skyline Reporting with Linear…
We present several new results on one of the most extensively studied topics in computational geometry, orthogonal range searching. All our results are in the standard word RAM model for points in rank space: ** We present two data…
In this paper we study the four-dimensional dominance range reporting problem and present data structures with linear or almost-linear space usage. Our results can be also used to answer four-dimensional queries that are bounded on five…
We study the following problem: preprocess a set O of objects into a data structure that allows us to efficiently report all pairs of objects from O that intersect inside an axis-aligned query range Q. We present data structures of size…
In this paper, we address the minimum-area rectangular and square annulus problem, which asks a rectangular or square annulus of minimum area, either in a fixed orientation or over all orientations, that encloses a set $P$ of $n$ input…
We consider several problems that involve lines in three dimensions, and present improved algorithms for solving them. The problems include (i) ray shooting amid triangles in $R^3$, (ii) reporting intersections between query lines…
Ranking (or top-k) and skyline queries are the most popular approaches used to extract interesting data from large datasets. The first one is based on a scoring function to evaluate and rank tuples. Its computation is fast, but it is…
Considering a 2D matrix of positive and negative numbers, how might one draw a rectangle within it whose contents sum higher than all other rectangles'? This fundamental problem, commonly known the maximum rectangle problem or subwindow…
There is a high demand of space-efficient algorithms in built-in or embedded softwares. In this paper, we consider the problem of designing space-efficient algorithms for computing the maximum area empty rectangle (MER) among a set of…
This paper presents a new application for multi-dimensional Skyline query. The idea presented in this paper can be used to find best shopping malls based on users requirements. A web-based application was used to simulate the problem and…
Multi-criteria decision making has been made possible with the advent of skyline queries. However, processing such queries for high dimensional datasets remains a time consuming task. Real-time applications are thus infeasible, especially…
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…
Recent studies pointed out some limitations about classic top-k queries and skyline queries. Ranking queries impose the user to provide a specific scoring function, which can lead to the exclusion of interesting results because of the…
Multi-objective optimization is the problem of optimizing simultaneously multiple objective functions and several techniques exist to deal with this problem. This paper aims to present the main methods that can be used to solve this issue…
Shallow cuttings are a fundamental tool in computational geometry and spatial databases for solving offline and online range searching problems. For a set $P$ of $N$ points in 3-D, at SODA'14, Afshani and Tsakalidis designed an optimal…
Given a set $P$ of $n$ points on $\mathbb R^{2}$, we address the problem of computing an axis-parallel empty rectangular annulus $A$ of maximum-width such that no point of $P$ lies inside $A$ but all points of $P$ must lie inside, outside…
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…
The problem of optimizing across different, conceivably conflicting, criteria is called multi-objective optimization and it is widely spread across many fields. This is a recurring problem in database queries when there is the need of…
This work studies the problem of 2-dimensional searching for the 3-sided range query of the form $[a, b]\times (-\infty, c]$ in both main and external memory, by considering a variety of input distributions. We present three sets of…
In the polytope membership problem, a convex polytope $K$ in $R^d$ is given, and the objective is to preprocess $K$ into a data structure so that, given a query point $q \in R^d$, it is possible to determine efficiently whether $q \in K$.…
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 $S$…