Lower Bounds for the Complexity of the Hausdorff Distance
نویسنده
چکیده
We describe new lower bounds for the complexity of the directed Hausdorr distance under translation and rigid motion. We exhibit lower bound constructions of (n 3) for point sets under translation, for the L 1 , L 2 and L 1 norms, (n 4) for line segments under translation , for any L p norm, (n 5) for point sets under rigid motion and (n 6) for line segments under rigid motion, both for the L 2 norm. The results for point sets can also be extended to the undirected Hausdorr distance.
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