2 research outputs found
On characteristic points and approximate decision algorithms for the minimum Hausdorff distance
We investigate {\em approximate decision algorithms} for determining whether the minimum Hausdorff distance between two points sets (or between two sets of nonintersecting line segments) is at most .\def\eg{(\varepsilon/\gamma)} An approximate decision algorithm is a standard decision algorithm that answers {\sc yes} or {\sc no} except when is in an {\em indecision interval} where the algorithm is allowed to answer {\sc don't know}. We present algorithms with indecision interval where is the minimum Hausdorff distance and can be chosen 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 cardinalities and our approximate decision algorithms run in time O(\eg^2(m+n)\log(mn)) for Hausdorff distance under translation, and in time O(\eg^2mn\log(mn)) for Hausdorff distance under Euclidean motion
The translation square map and approximate congruence
This paper published in "Operations Research" 41 (1993), 947-95