Learn More
Motivated by the problem of labeling maps, we i n vestigate the problem of computing a large non-intersecting subset in a set of n rectangles in the plane. Our results are as follows. In On log n time, we can nd an Olog n-factor approximation of the maximum subset in a set of n arbitrary axis-parallel rectangles in the plane. If all rectangles have unit(More)
For 2D or 3D meshes that represent the domain of continuous function to the reals, the contours|or isosurfaces|of a speciied value are an important w ay to visualize the function. To nd such contours, a seed set can be used for the starting points from which the traversal of the contours can begin. This paper gives the rst methods to obtain seed sets that(More)
For a set P of points in the plane, we introduce a class of triangulations that is an extension of the Delaunay triangulation. Instead of requiring that for each triangle the circle through its vertices contains no points of P inside, we require that at most k points are inside the circle. Since there are many different higher-order Delaunay triangulations(More)
Moving point object data can be analyzed through the discovery of patterns. We consider the computational efficiency of computing two of the most basic spatio-temporal patterns in trajectories, namely flocks and meetings. The patterns are large enough subgroups of the moving point objects that exhibit similar movement and proximity for a certain amount of(More)
In this paper we study several instances of the problem of determining the maximum number of topologically distinct two-dimensional images that three-dimensional scenes can induce. To bound this number, we investigate arrangements of curves and of surfaces that have a certain sparseness property. Given a collection of n algebraic surface patches of constant(More)
In geographic information retrieval, queries often use names of geographic regions that do not have a well-defined boundary, such as " Southern France. " We provide two classes of algorithms for the problem of computing reasonable boundaries of such regions, based on evidence of given data points that are deemed likely to lie either inside or outside the(More)
Road network analysis can require distance from points that are not on the network themselves. We study the algorithmic problem of connecting a point inside a face (region) of the road network to its boundary while minimizing the detour factor of that point to any point on the boundary of the face. We show that the optimal single connection (feed-link) can(More)
General Terms: add here 1. INTRODUCTION A large proportion of the resources available on the worldwide web refer to information that may be regarded as geographically located. Thus most activities and enterprises take place in one or more places on the Earth's surface and there is a wealth of survey data, images, maps and reports that relate to specific(More)
A rectangular cartogram is a type of map where every region is a rectangle. The size of the rectangles is chosen such that their areas represent a geographic variable (e.g., population). Good rectangular cartograms are hard to generate: The area specifications for each rectangle may make it impossible to realize correct adjacencies between the regions and(More)