A crucial task on these objects is to measure their similarity.
Therefore, this thesis presents results on algorithms, complexity lower bounds, and algorithm engineering of the most important point set and sequence similarity measures like the Fréchet distance, the Fréchet distance under translation, and the Hausdorff distance under translation.
As an extension to the mere computation of similarity, also the approximate near neighbor problem for the continuous Fréchet distance on time series is considered and matching upper and lower bounds are shown.
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