The algebraic degree of geometric optimization problems
Discrete & Computational Geometry
Stabbing parallel segments with a convex polygon
Computer Vision, Graphics, and Image Processing
Structural tolerance and delauny triangulation
Information Processing Letters
Precision-Sensitive Euclidean Shortest Path in 3-Space
SIAM Journal on Computing
Tight Error Bounds of Geometric Problems on Convex Objects with Imprecise Coordinates
JCDCG '00 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
Convex Hulls of Bounded Curvature
Proceedings of the 8th Canadian Conference on Computational Geometry
Touring a sequence of polygons
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Almost-Delaunay simplices: nearest neighbor relations for imprecise points
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Systems of distant representatives
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Triangulating input-constrained planar point sets
Information Processing Letters
Approximating largest convex hulls for imprecise points
WAOA'07 Proceedings of the 5th international conference on Approximation and online algorithms
Largest bounding box, smallest diameter, and related problems on imprecise points
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
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Assume that a set of imprecise points is given, where each point is specified by a region in which the point may lie. We study the problem of computing the smallest and largest possible tours and convex hulls, measured by length, and in the latter case also by area. Generally we assume the imprecision region to be a square, but we discuss the case where it is a segment or circle as well. We give polynomial time algorithms for several variants of this problem, ranging in running time from O(n) to O(n13), and prove NP-hardness for some geometric problems on imprecise points