Covering convex sets with non-overlapping polygons
Discrete Mathematics
Fuzzy geometry: an updated overview
Information Sciences: an International Journal
Structural tolerance and delauny triangulation
Information Processing Letters
Almost-Delaunay simplices: nearest neighbor relations for imprecise points
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Acute Triangulations of Polygons
Discrete & Computational Geometry
Triangulating input-constrained planar point sets
Information Processing Letters
Computing hereditary convex structures
Proceedings of the twenty-fifth annual symposium on Computational geometry
Delaunay triangulation of imprecise points in linear time after preprocessing
Computational Geometry: Theory and Applications
Three problems about simple polygons
Computational Geometry: Theory and Applications
Largest bounding box, smallest diameter, and related problems on imprecise points
Computational Geometry: Theory and Applications
On constrained minimum pseudotriangulations
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
Closest pair and the post office problem for stochastic points
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Nearest-neighbor searching under uncertainty
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
Self-improving algorithms for coordinate-wise maxima
Proceedings of the twenty-eighth annual symposium on Computational geometry
Convex hull of points lying on lines in o(nlogn) time after preprocessing
Computational Geometry: Theory and Applications
Unions of onions: preprocessing imprecise points for fast onion layer decomposition
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
Closest pair and the post office problem for stochastic points
Computational Geometry: Theory and Applications
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Traditional algorithms in computational geometry assume that the input points are given precisely. In practice, data is usually imprecise, but information about the imprecision is often available. In this context, we investigate what the value of this information is. We show here how to preprocess a set of disjoint regions in the plane of total complexity $n$ in $O(n\log n)$ time so that if one point per set is specified with precise coordinates, a triangulation of the points can be computed in linear time. In our solution, we solve another problem which we believe to be of independent interest. Given a triangulation with red and blue vertices, we show how to compute a triangulation of only the blue vertices in linear time.