Faster DB-scan and HDB-scan in low-dimensional Euclidean spaces

We present a new algorithm for the widely used density-based clustering method DBscan. Our algorithm computes the DBscan-clustering in O(nlogn) time in R 2 , irrespective of the scale parameter ε (and assuming the second parameter MinPts is set to a fixed constant, as is the case in practice). Experiments show that the new algorithm is not only fast in theory, but that a slightly simplified version is competitive in practice and much less sensitive to the choice of ε than the original DBscan algorithm. We also present an O(nlogn) randomized algorithm for HDBscan in the plane---HDBscan 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.