Delaunay Triangulation of Imprecise Points Simplified and Extended
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Competitive query strategies for minimising the ply of the potential locations of moving points
Proceedings of the twenty-ninth annual symposium on Computational geometry
Unions of onions: preprocessing imprecise points for fast onion layer decomposition
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
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We consider the problems of computing maximal points and the convex hull of a set of points in two dimensions, when the points are “in motion.” We assume that the point locations (or trajectories) are not known precisely and determining these values exactly is feasible, but expensive. In our model the algorithm only knows areas within which each of the input points lie, and is required to identify the maximal points or points on the convex hull correctly by updating some points (i.e., determining their location exactly). We compare the number of points updated by the algorithm on a given instance to the minimum number of points that must be updated by a nondeterministic strategy in order to compute the answer provably correctly. We give algorithms for both of the above problems that always update at most three times as many points as the nondeterministic strategy, and show that this is the best possible. Our model is similar to that in [3] and [5].