Related papers: Computation of Spatial Skyline Points
We present a new algorithm that produces a well-spaced superset of points conforming to a given input set in any dimension with guaranteed optimal output size. We also provide an approximate Delaunay graph on the output points. Our…
An efficient computer algorithm is described for the perspective drawing of a wide class of surfaces. The class includes surfaces corresponding lo single-valued, continuous functions which are defined over rectangular domains. The algorithm…
We study the problem of estimating the value of sums of the form $S_p \triangleq \sum \binom{x_i}{p}$ when one has the ability to sample $x_i \geq 0$ with probability proportional to its magnitude. When $p=2$, this problem is equivalent to…
Finding approximate stationary points, i.e., points where the gradient is approximately zero, of non-convex but smooth objective functions $f$ over unrestricted $d$-dimensional domains is one of the most fundamental problems in classical…
A mixed dominating set of a graph $G = (V, E)$ is a mixed set $D$ of vertices and edges, such that for every edge or vertex, if it is not in $D$, then it is adjacent or incident to at least one vertex or edge in $D$. The mixed domination…
There are many space subdivision and space partitioning techniques used in many algorithms to speed up computations. They mostly rely on orthogonal space subdivision, resp. using hierarchical data structures, e.g. BSP trees, quadtrees,…
Given a set $P$ of $n$ points and a set $S$ of $m$ disks in the plane, the disk coverage problem asks for a smallest subset of disks that together cover all points of $P$. The problem is NP-hard. In this paper, we consider a line-separable…
We study partial and budgeted versions of the well studied connected dominating set problem. In the partial connected dominating set problem, we are given an undirected graph G = (V,E) and an integer n', and the goal is to find a minimum…
The most common archetypes to identify relevant information in large datasets and find the bestoptions according to some preferences or user criteria, are the top-k queries (ranking method based ona score function defined over the records…
We present a new approach to approximate nearest-neighbor queries in fixed dimension under a variety of non-Euclidean distances. We are given a set $S$ of $n$ points in $\mathbb{R}^d$, an approximation parameter $\varepsilon > 0$, and a…
Satellite imagery solutions are widely used to study and monitor different regions of the Earth. However, a single satellite image can cover only a limited area. In cases where a larger area of interest is studied, several images must be…
The reachable sets of nonlinear control systems can in general only be numerically approximated, and are often very expensive to calculate. In this paper, we propose an algorithm that tracks only the boundaries of the reachable sets and…
Given a graph $G=(V,E)$, a vertex $u \in V$ {\em ve-dominates} all edges incident to any vertex of $N_G[u]$. A set $S \subseteq V$ is a {\em ve-dominating set} if for all edges $e\in E$, there exists a vertex $u\in S$ such that $u$…
Let $P$ be a simple polygon with $n$ vertices, and let $A$ be a set of $m$ points or line segments inside $P$. We develop data structures that can efficiently count the number of objects from $A$ that are visible to a query point or a query…
Given two point sets in the plane, we study the minimization of the bottleneck distance between a point set B and an equally-sized subset of a point set A under translations. We relate this problem to a Voronoi-type diagram and derive…
Subspace clustering is an important unsupervised clustering approach. It is based on the assumption that the high-dimensional data points are approximately distributed around several low-dimensional linear subspaces. The majority of the…
Capacitated Domination generalizes the classic Dominating Set problem by specifying for each vertex a required demand and an available capacity for covering demand in its closed neighborhood. The objective is to find a minimum-sized set of…
Consider a set $P$ of $n$ points picked uniformly and independently from $[0,1]^d$ for a constant dimension $d$ -- such a point set is extremely well behaved in many aspects. For example, for a fixed $r \in [0,1]$, we prove a new…
Given a countable set of points in a continuous space, Voronoi tessellation is an intuitive way of partitioning the space according to the distance to the individual points. As a powerful approach to obtain structural information, it has a…
This paper introduces a novel approach to solve the coverage optimization problem in multi-agent systems. The proposed technique offers an optimal solution with a lower cost with respect to conventional Voronoi-based techniques by…