Marta Fort

Multi-visibility maps of triangulated terrains

Visibility computation on terrain models is an important research topic with many applications in Geographical Information Systems. A multi‐visibility map is the subdivision of the domain of a terrain into regions that, according to different criteria, encodes the visibility with respect to a set of view elements. We present an approach for visualising approximated multi‐visibility maps of a triangulated terrain corresponding to a set of view elements by using graphics hardware. Our method supports heterogeneous sets of view elements containing points, segments, polygonal chains and polygons and works for weak and strong visibility. Moreover, we are also able to efficiently solve approximated point and polygonal region multi‐visibility queries. To illustrate the usefulness of our approach we present results obtained with an implementation of the proposed algorithms.

Higher-order Voronoi diagrams on triangulated surfaces

We study the complexity of higher-order Voronoi diagrams on triangulated surfaces under the geodesic distance, when the sites may be polygonal domains of constant complexity. More precisely, we show that on a surface defined by n triangles the sum of the combinatorial complexities of the order-j Voronoi diagrams of m sites, for j=1,...,k, is O(k^2n^2+k^2m+knm), which is asymptotically tight in the worst case.

Solving the k-influence region problem with the GPU

In this paper we study a problem that arises in the competitive facility location field. Facilities and customers are represented by points of a planar Euclidean domain. We associate a weighted distance to each facility to reflect that customers select facilities depending on distance and importance. We define, by considering weighted distances, the k-influence region of a facility as the set of points of the domain that has the given facility among their k-nearest/farthest neighbors. On the other hand, we partition the domain into subregions so that each subregion has a non-negative weight associated to it which measures a characteristic related to the area of the subregion. Given a weighted partition of the domain, the k-influence region problem finds the points of the domain where are new facility should be opened. This is done considering the known weight associated to the new facility and ensuring a minimum weighted area of its k-influence region. We present a GPU parallel approach, designed under CUDA architecture, for approximately solving the k-influence region problem. In addition, we describe how to visualize the solutions, which improves the understanding of the problem and reveals complicated structures that would be hard to capture otherwise. Integration of computation and visualization facilitates decision makers with an iterative what-if analysis process, to acquire more information to obtain an approximate optimal location. Finally, we provide and discuss experimental results showing the efficiency and scalability of our approach.

Finding extremal sets on the GPU

The extremal sets of a family F of sets consist of all sets of F that are maximal or minimal with respect to the partial order induced by the subset relation in F . In this paper we present efficient parallel GPU-based algorithms, designed under CUDA architecture, for finding the extremal sets of a family F of sets. The complexity analysis of the presented algorithms together with experimental results showing the efficiency and scalability of the approach is provided. We present parallel algorithms designed under CUDA for finding the extremal sets of a family F of sets.We solve either the maximal or the minimal sets problem.The complexity analysis of the presented algorithms is provided.Algorithms are experimentally tested and several results are provided.

Finding influential location regions based on reverse k -neighbor queries

In this paper we introduce and solve several problems that arise in the single facility location field. A reverse k-influential location problem finds a region such that the location of a new facility, desirable or obnoxious, in the region guarantees a minimum k-influential value associated to the importance, attractiveness or repulsiveness, of the facility as a solution to a reverse k-nearest or farthest neighbor query. Solving reverse k-influential location problems help decision makers to progress towards suitable locations for a new facility. We present a parallel approach, to be ran on a graphics processing unit, for approximately solving reverse k-influential location problems, and also provide and discuss experimental results showing the efficiency and scalability of our approach.

Computing and visualizing popular places

Data analysis and knowledge discovery in trajectory databases is an emerging field with a growing number of applications such as managing traffic, planning tourism infrastructures, analyzing professional sport matches or better understanding wildlife. A well-known collection of patterns which can occur for a subset of trajectories of moving objects exists. In this paper, we study the popular places pattern, that is, locations that are visited by many moving objects. We consider two criteria, strong and weak, to establish either the exact number of times that an object has visited a place during its complete trajectory or whether it has visited the place, or not. To solve the problem of reporting popular places, we introduce the popularity map. The popularity of a point is a measure of how many times the moving objects of a set have visited that point. The popularity map is the subdivision, into regions, of a plane where all the points have the same popularity. We propose different algorithms to efficiently compute and visualize popular places, the so-called popular regions and their schematization, by taking advantage of the parallel computing capabilities of the graphics processing units. Finally, we provide and discuss the experimental results obtained with the implementation of our algorithms.

A parallel GPU-based approach for reporting flock patterns

Data analysis and knowledge discovery in trajectory databases is an emerging field with a growing number of applications such as managing traffic, planning tourism infrastructures or better understanding wildlife. In this paper, we study the problem of finding flock patterns in trajectory databases. A flock refers to a large enough subset of entities that move close to each other for, at least, a given time interval. We present parallel algorithms, to be run on a Graphics Processing Unit, for reporting three different variants of the flock pattern: (1) all maximal flocks, (2) the largest flock and (3) the longest flock. We also provide their complexity analysis together with experimental results showing the efficiency and scalability of our approach.

GPU-Based influence regions optimization

In this paper we introduce an optimization problem, that arises in the competitive facility location area, which involves the maximization of the weighted area of the region where a new facility has influence. We consider a finite set of points S in a bounded polygonal region domain D subdivided into several non-negative weighted regions according to a weighted domain partition

Computing Popular Places Using Graphics Processors

\mathcal{P}

Generalized Higher-Order Voronoi Diagrams on Polyhedral Surfaces

. For each point in S we define its k-nearest/farthest neighbor influence region as the region containing all the points of D having the considered point as one of their k-nearest/farthest neighbors in S. We want to find a new point s in D whose k-influence region is maximal in terms of weighted area according to the weighted partition