On Characteristic Points and Approximate Decision Algorithms for the Minimum Hausdor Distance

We investigate approximate decision algorithms for determining whether the mini mumHausdor distance between two points sets or between two sets of nonintersecting line segments is at most An approximate decision algorithm is a standard decision algorithm that answers yes or no except when is in an indecision interval where the algorithm is allowed to answer don t know We present algorithms with indecision interval where is the minimum Hausdor distance and can be cho sen by the user In other words we can make our algorithm as accurate as desired by choosing an appropriate For two sets of points or two sets of nonintersecting lines with respective cardinalitiesm and n our approximate decision algorithms run in time O m n log mn for Hausdor distance under translation and in time O mn log mn for Hausdor distance under Euclidean motion