We present a new algorithm for the widely used density-based clustering method DBScan. Our algorithm computes the DBScan-clustering in O(n log n) time in R^2, irrespective of the scale parameter \eps, but assuming the second parameter MinPts is set to a fixed constant, as is the case in practice. We also present an O(n log n) randomized algorithm for HDBScan in the plane---HDBScans is a hierarchical version of DBScan introduced recently---and we show how to compute an approximate version of HDBScan in near-linear time in any fixed dimension.
@InProceedings{deberg_et_al:LIPIcs.ISAAC.2017.25, author = {de Berg, Mark and Gunawan, Ade and Roeloffzen, Marcel}, title = {{Faster DBScan and HDBScan in Low-Dimensional Euclidean Spaces}}, booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)}, pages = {25:1--25:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-054-5}, ISSN = {1868-8969}, year = {2017}, volume = {92}, editor = {Okamoto, Yoshio and Tokuyama, Takeshi}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.25}, URN = {urn:nbn:de:0030-drops-82102}, doi = {10.4230/LIPIcs.ISAAC.2017.25}, annote = {Keywords: Density-based clustering, hierarchical clustering} }
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