2026-10-09T01:45:45Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:8769 2024-03-06T09:42:36Z ddc:004 open_access

On Optimal Polyline Simplification Using the Hausdorff and Fréchet Distance van Kreveld, Marc Löffler, Maarten Wiratma, Lionov polygonal line simplification Hausdorff distance Fréchet distance Imai-Iri Douglas-Peucker We revisit the classical polygonal line simplification problem and study it using the Hausdorff distance and Fréchet distance. Interestingly, no previous authors studied line simplification under these measures in its pure form, namely: for a given epsilon>0, choose a minimum size subsequence of the vertices of the input such that the Hausdorff or Fréchet distance between the input and output polylines is at most epsilon. We analyze how the well-known Douglas-Peucker and Imai-Iri simplification algorithms perform compared to the optimum possible, also in the situation where the algorithms are given a considerably larger error threshold than epsilon. Furthermore, we show that computing an optimal simplification using the undirected Hausdorff distance is NP-hard. The same holds when using the directed Hausdorff distance from the input to the output polyline, whereas the reverse can be computed in polynomial time. Finally, to compute the optimal simplification from a polygonal line consisting of n vertices under the Fréchet distance, we give an O(kn^5) time algorithm that requires O(kn^2) space, where k is the output complexity of the simplification. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Marc van Kreveld and Maarten Löffler and Lionov Wiratma 2018 Is Part Of LIPIcs, Volume 99, 34th International Symposium on Computational Geometry (SoCG 2018) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2018.56 urn:nbn:de:0030-drops-87694 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2018.56 eng https://creativecommons.org/licenses/by/3.0/legalcode