Optimal algorithms for approximate clustering
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Epsilon geometry: building robust algorithms from imprecise computations
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Stabbing parallel segments with a convex polygon
Computer Vision, Graphics, and Image Processing
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Approximate decision algorithms for point set congruence
Computational Geometry: Theory and Applications
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
On intersecting a set of parallel line segments with a convex polygon of minimum area
Information Processing Letters
On intersecting a set of isothetic line segments with a convex polygon of minimum area
ICCSA'07 Proceedings of the 2007 international conference on Computational science and its applications - Volume Part I
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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We consider the directed Hausdorff distance between point sets in the plane, where one or both point sets consist of imprecise points. An imprecise point is modelled by a disc given by its centre and a radius. The actual position of an imprecise point may be anywhere within its disc. Due to the direction of the Hausdorff Distance and whether its tight upper or lower bound is computed there are several cases to consider. For every case we either show that the computation is NP-hard or we present an algorithm with a polynomial running time. Further we give several approximation algorithms for the hard cases and show that one of them cannot be approximated better than with factor 3, unless P=NP.