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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)
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)
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)
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)
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)
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)
We introduce the concept of subdivision drawings of hyper-graphs. In a subdivision drawing each vertex corresponds uniquely to a face of a planar subdivision and, for each hyperedge, the union of the faces corresponding to the vertices incident to that hyperedge is connected. Vertex-based Venn diagrams and concrete Euler diagrams are both subdivision(More)